A stochastic numerical approach for a class of singular singularly perturbed system

Zulqurnain Sabir; Thongchai Botmart; Muhammad Asif Zahoor Raja; Wajaree Weera; Fevzi Erdoğan

doi:10.1371/journal.pone.0277291

Peer Review History

Original SubmissionDecember 9, 2021
14 Mar 2022 Decision Letter - Chengming Huang, Editor PONE-D-21-38900A stochastic numerical approach for a class of singular singularly perturbed systemPLOS ONE Dear Dr. Botmart, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Apr 28 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols. We look forward to receiving your revised manuscript. Kind regards, Chengming Huang Academic Editor PLOS ONE Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. Thank you for stating the following financial disclosure: “The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.” At this time, please address the following queries: a) Please clarify the sources of funding (financial or material support) for your study. List the grants or organizations that supported your study, including funding received from your institution. b) State what role the funders took in the study. If the funders had no role in your study, please state: “The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.” c) If any authors received a salary from any of your funders, please state which authors and which funders. d) If you did not receive any funding for this study, please state: “The authors received no specific funding for this work.” Please include your amended statements within your cover letter; we will change the online submission form on your behalf. 3. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability. Upon re-submitting your revised manuscript, please upload your study’s minimal underlying data set as either Supporting Information files or to a stable, public repository and include the relevant URLs, DOIs, or accession numbers within your revised cover letter. For a list of acceptable repositories, please see http://journals.plos.org/plosone/s/data-availability#loc-recommended-repositories. Any potentially identifying patient information must be fully anonymized. Important: If there are ethical or legal restrictions to sharing your data publicly, please explain these restrictions in detail. Please see our guidelines for more information on what we consider unacceptable restrictions to publicly sharing data: http://journals.plos.org/plosone/s/data-availability#loc-unacceptable-data-access-restrictions. Note that it is not acceptable for the authors to be the sole named individuals responsible for ensuring data access. We will update your Data Availability statement to reflect the information you provide in your cover letter. 4. We note you have included a table to which you do not refer in the text of your manuscript. Please ensure that you refer to table 2 in your text; if accepted, production will need this reference to link the reader to the Table. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: Yes ****** 4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes ****** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: A stochastic numerical approach for a class of singular singularly perturbed system In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO), and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions, and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness, and accuracy. As we all know, the models based on the singular systems are advantageous, and the solution of such models by using stochastic schemes is also appreciable. The ANNs methods are crucial and have considerable applications in diverse fields After carefully reviewing the paper, I conclude that: • Paper is interesting • Results are mathematically correct • Presentation is also nice However, the paper can be accepted for publication after considering the following minor revisions as follows: 1)The introduction is written well, but add a few more recent applications for improvement, for instance: https://doi.org/10.1016/j.asej.2020.11.007 https://doi.org/10.1371/journal.pone.0235829 10.1109/ACCESS.2021.3078750 https://doi.org/10.1155/2022/9660746 10.1109/ACCESS.2021.3133815 2) Adjust statistical performance measures in section 2 3) Use proper punctuation 4) Use the same style of references 5) What effects can be seen by increasing or decreasing the neurons 6) Mention a few applications of IPA. Reviewer #2: In this paper, a method based on numerical approach is developed for solving singularly perturbed system. This paper will be recommended for publication after some revisions. Comments: 1. Complexity: Please give some theoretical analysis in the time complexity of the current paper. 2. Authors improve the grammar in the manuscript. 3. Authors should add error analysis in details of proposed method. 4. To verify the convergence and efficiency of the method it would be very important to show how the error changes as I increase. I think that such tables should be presented. 5. I think that the numerical results presented are not sufficient to convince the reader about the advantage of the method. 6. The list of references is quite poor and it should be enlarged. ****** 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review?** For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0277291.r001
Revision 1
21 Apr 2022 Author Response Author Response Paper Title: A stochastic numerical approach for a class of singular singularly perturbed system By: Zulqurnain Sabir, Thongchai Botmart, Muhammad Asif Zahoor Raja, Wajaree weera, Fevzi Erdoğan ID: PONE-D-21-38900, Journal: PLOS ONE Reviewers' comments: Reviewer 1: General comments In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm optimization (PSO), and local search interior-point algorithm (IPA), i.e., ANNs-PSO-IPA. An error-based fitness function is designed using the differential form of the SSP-BVPs and its boundary conditions. The optimization of this fitness function is performed by using the computing capabilities of ANNs-PSO-IPA. Four cases of two SSP systems are tested to confirm the performance of the suggested ANNs-PSO-IPA. The correctness of the scheme is observed by using the comparison of the proposed and the exact solutions. The performance indices through different statistical operators are also provided to solve the SSP-BVPs using the proposed ANNs-PSO-IPA. Moreover, the reliability of the scheme is observed by taking hundred independent executions, and different statistical performances have been provided for solving the SSP-BVPs to check the convergence, robustness, and accuracy. As we all know, the models based on the singular systems are advantageous, and the solution of such models by using stochastic schemes is also appreciable. The ANNs methods are crucial and have considerable applications in diverse fields After carefully reviewing the paper, I conclude that: • Paper is interesting • Results are mathematically correct • Presentation is also nice However, the paper can be accepted for publication after considering the following minor revisions as follows: Authors reply First of all, many thanks for your valuable remarks “As we all know, the models based on the singular systems are advantageous, and the solution of such models by using stochastic schemes is also appreciable. The ANNs methods are crucial and have considerable applications in diverse fields After carefully reviewing the paper, I conclude that: • Paper is interesting • Results are mathematically correct • Presentation is also nice” and favorable recommendation “the paper can be accepted for publication after considering the following minor revisions” on our submitted manuscript. Moreover, the authors tried level best to address all the valuable suggestions of the worthy anonymous reviewer and modified the manuscript accordingly. Query 1 1) The introduction is written well, but add a few more recent applications for improvement, for instance: https://doi.org/10.1016/j.asej.2020.11.007 https://doi.org/10.1371/journal.pone.0235829 10.1109/ACCESS.2021.3078750 https://doi.org/10.1155/2022/9660746 10.1109/ACCESS.2021.3133815 Authors Reply Agreed. We have updated the manuscript by providing the exhaustive literature review in the introduction section to portray the problem statement with justification with the help of relevant, recent and reputed journal articles as suggested. Many thanks for suggesting the relevant recent articles [r1-r8] on the topic and indeed these article are very helpful to improve the technical and presentation strength of the introduction section. [r1] Ahmad, A., Sulaiman, M., Aljohani, A.J., Alhindi, A. and Alrabaiah, H., 2021. Design of an efficient algorithm for solution of Bratu differential equations. Ain Shams Engineering Journal, 12(2), pp.2211-2225. [r2] Waseem, W., Sulaiman, M., Kumam, P., Shoaib, M., Raja, M.A.Z. and Islam, S., 2020. Investigation of singular ordinary differential equations by a neuroevolutionary approach. Plos one, 15(7), p.e0235829. [r3] Zhang, Y., Lin, J., Hu, Z., Khan, N.A. and Sulaiman, M., 2021. Analysis of third-order nonlinear multi-singular Emden–Fowler equation by using the LeNN-WOA-NM algorithm. IEEE Access, 9, pp.72111-72138. [r4] Fawad Khan, M., Bonyah, E., Alshammari, F.S., Ghufran, S.M. and Sulaiman, M., 2022. Modelling and Analysis of Virotherapy of Cancer Using an Efficient Hybrid Soft Computing Procedure. Complexity, 2022. [r5] Rahman, I.U., Sulaiman, M., Alarfaj, F.K., Kumam, P. and Laouini, G., 2021. Investigation of Non-Linear MHD Jeffery–Hamel Blood Flow Model Using a Hybrid Metaheuristic Approach. IEEE Access, 9, pp.163214-163232. [r6] Bukhari, A.H., Raja, M.A.Z., Sulaiman, M., Islam, S., Shoaib, M. and Kumam, P., 2020. Fractional neuro-sequential ARFIMA-LSTM for financial market forecasting. IEEE Access, 8, pp.71326-71338. [r7] Bukhari, A.H., Sulaiman, M., Raja, M.A.Z., Islam, S., Shoaib, M. and Kumam, P., 2020. Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system. Alexandria Engineering Journal, 59(5), pp.3325-3345. [r8] Bukhari, A.H., Sulaiman, M., Islam, S., Shoaib, M., Kumam, P. and Raja, M.A.Z., 2020. Neuro-fuzzy modeling and prediction of summer precipitation with application to different meteorological stations. Alexandria Engineering Journal, 59(1), pp.101-116. Query 2 2) Adjust statistical performance measures in section 2 Authors reply Agreed. We have updated the manuscript by the adjusting the statistical performance measures in section 2 as suggested. Query 3 3) Use proper punctuation Authors reply Agreed. We have updated the manuscript by careful review of the inserted punctuations in the whole draft as suggested. Query 4 4) Use the same style of references Authors reply Agreed. We have updated the manuscript by all the references on consistent template as suggested. Query 5 5) What effect can be seen by increasing or decreasing the neurons Authors reply By increasing the number of neurons, the a slight improvement in the accuracy is achieved but at the cost of additional computations and also arises an issue of overfitting. Query 6 6) Mention a few applications of IPA. Authors reply Agreed. We have updated the manuscript by mentioning the applications of the IPA as suggested. Reviewer 2 General Comments Reviewer #2: In this paper, a method based on numerical approach is developed for solving singularly perturbed system. This paper will be recommended for publication after some revisions. Authors reply First of all, many thanks for your valuable remarks “a method based on numerical approach is developed for solving singularly perturbed system” and favorable recommendations “recommended for publication after some revisions” on our submitted manuscript. Additionally, the authors tried their level best to address all the changes suggested by the worthy anonymous reviewer and the manuscript is modified accordingly. Comment 1 1. Complexity: Please give some theoretical analysis in the time complexity of the current paper. Authors reply Agreed. We have updated the manuscript by providing the necessary information regarding the complexity in the results section of the revised manuscript. Please see the complexity information presented in highlighted Tables 7 and 8 along with the interpretations in the results section of the revised manuscript. Comment 2 2. Authors improve the grammar in the manuscript. Authors reply Agreed. We have updated the manuscript by critical, careful and exhaustive review of the whole draft to improve the linguistic quality by avoiding the grammatical errors, ambiguous sentences, and typos as suggested by the worthy anonymous reviewer for better understanding of the readers. Comment 3 3. Authors should add error analysis in details of proposed method. Authors reply Agreed. We have updated the manuscript by providing the rigorous error analysis from the available reference solutions for the both problems in terms of difference performance indices in order to portray the inferences and worth of the design methodology as suggested for better understanding of readers. Comment 4 4. To verify the convergence and efficiency of the method it would be very important to show how the error changes as I increase. I think that such tables should be presented. Authors reply Agreed. We have updated the manuscript by providing information regarding the convergence and efficient more elaborative on the basis on single and multiple runs of the presented scheme as suggested. In this study, the accuracy, convergence, stability and robustness of the presented scheme is endorsed with the help of rigorous statistics via performance measure on the basis of mean absolute deviation (MAD), Theil’s inequality coefficient (TIC) operator and Nash Sutcliffe efficiency (NSE) operator as well as global MAD, Global TIC and Global NSE are applied to solve SSP-BVPs for all cases of both problems. Please see the results section of the revised manuscript.. Comment 5 5. I think that the numerical results presented are not sufficient to convince the reader about the advantage of the method. Authors reply Agreed. We have updated the manuscript by providing the necessary elaborative information of the simulations along with their statistical assessments and complexity studies in the results section to facilitate the reader more clearly to decipher the contributions of the study. Please see the updated simulation results presented in the results section. Comment 6 6. The list of references is quite poor and it should be enlarged. Authors Reply Agreed. We have updated the manuscript by providing the exhaustive literature review in the introduction section to portray the problem statement with justification with the help of relevant, recent and reputed journal articles as suggested. Many thanks for suggesting the relevant recent articles [r1-r18] on the topic and indeed these article are very helpful to improve the technical and presentation strength of the introduction section. [r1] Ahmad, A., Sulaiman, M., Aljohani, A.J., Alhindi, A. and Alrabaiah, H., 2021. Design of an efficient algorithm for solution of Bratu differential equations. Ain Shams Engineering Journal, 12(2), pp.2211-2225. [r2] Waseem, W., Sulaiman, M., Kumam, P., Shoaib, M., Raja, M.A.Z. and Islam, S., 2020. Investigation of singular ordinary differential equations by a neuroevolutionary approach. Plos one, 15(7), p.e0235829. [r3] Zhang, Y., Lin, J., Hu, Z., Khan, N.A. and Sulaiman, M., 2021. Analysis of third-order nonlinear multi-singular Emden–Fowler equation by using the LeNN-WOA-NM algorithm. IEEE Access, 9, pp.72111-72138. [r4] Fawad Khan, M., Bonyah, E., Alshammari, F.S., Ghufran, S.M. and Sulaiman, M., 2022. Modelling and Analysis of Virotherapy of Cancer Using an Efficient Hybrid Soft Computing Procedure. Complexity, 2022. [r5] Rahman, I.U., Sulaiman, M., Alarfaj, F.K., Kumam, P. and Laouini, G., 2021. Investigation of Non-Linear MHD Jeffery–Hamel Blood Flow Model Using a Hybrid Metaheuristic Approach. IEEE Access, 9, pp.163214-163232. [r6] Bukhari, A.H., Raja, M.A.Z., Sulaiman, M., Islam, S., Shoaib, M. and Kumam, P., 2020. Fractional neuro-sequential ARFIMA-LSTM for financial market forecasting. IEEE Access, 8, pp.71326-71338. [r7] Bukhari, A.H., Sulaiman, M., Raja, M.A.Z., Islam, S., Shoaib, M. and Kumam, P., 2020. Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system. Alexandria Engineering Journal, 59(5), pp.3325-3345. [r8] Bukhari, A.H., Sulaiman, M., Islam, S., Shoaib, M., Kumam, P. and Raja, M.A.Z., 2020. Neuro-fuzzy modeling and prediction of summer precipitation with application to different meteorological stations. Alexandria Engineering Journal, 59(1), pp.101-116. [r9] Guirao, J.L., Sabir, Z., Raja, M.A.Z. and Baleanu, D., 2022. Design of neuro-swarming computational solver for the fractional Bagley–Torvik mathematical model. The European Physical Journal Plus, 137(2), p.245. [r10] Sabir, Z., Raja, M.A.Z., Baleanu, D., Cengiz, K. and Shoaib, M., 2021. Design of Gudermannian Neuroswarming to solve the singular Emden–Fowler nonlinear model numerically. Nonlinear Dynamics, 106(4), pp.3199-3214. [r11] Iqbal, M.A., Fakhar, M.S., Kashif, S.A.R., Naeem, R. and Rasool, A., 2021. Impact of parameter control on the performance of APSO and PSO algorithms for the CSTHTS problem: An improvement in algorithmic structure and results. PloS one, 16(12), p.e0261562. [r12] Zhang, X. and Tang, Z., 2022. Construction of computer model for enterprise green innovation by PSO-BPNN algorithm and its impact on economic performance. Plos one, 17(1), p.e0262963. [r13] Hosseinzadeh Khonakdari, T. and Ahmadi Kamarposhti, M., 2021. Real-time detection of microgrid islanding considering sources of uncertainty using type-2 fuzzy logic and PSO algorithm. PloS one, 16(9), p.e0257830. [r14] Chen, F., Gao, X., Xia, X. and Xu, J., 2022. Using LSTM and PSO techniques for predicting moisture content of poplar fibers by Impulse-cyclone Drying. PloS one, 17(4), p.e0266186. [r15] Umar, M., Sabir, Z., Raja, M.A.Z., Amin, F., Saeed, T. and Guerrero-Sanchez, Y., 2021. Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19. Alexandria Engineering Journal, 60(3), pp.2811-2824. [r16] Sabir, Z., Raja, M.A.Z., Kamal, A., Guirao, J.L., Le, D.N., Saeed, T. and Salama, M., 2021. Neuro-Swarm heuristic using interior-point algorithm to solve a third kind of multi-singular nonlinear system. Mathematical Biosciences and Engineering, 18(5), pp.5285-5308. [r17] AlQadi, H. and Bani-Yaghoub, M., 2022. Incorporating global dynamics to improve the accuracy of disease models: Example of a COVID-19 SIR model. PloS one, 17(4), p.e0265815. [r18] Islam, M.Z., Othman, M.L., Abdul Wahab, N.I., Veerasamy, V., Opu, S.R., Inbamani, A. and Annamalai, V., 2021. Marine predators algorithm for solving single-objective optimal power flow. Plos one, 16(8), p.e0256050. Authors are once again thankful to anonymous reviewer, editor in chief, associate editor and editorial staff for their time, help, efforts and support. Best regards, Thongchai Botmart Corresponding author Attachments Attachment Submitted filename: Authors_Response_R1_PLOS-ONE.docx https://doi.org/10.1371/journal.pone.0277291.r002
30 Jun 2022 Decision Letter - Chengming Huang, Editor PONE-D-21-38900R1A stochastic numerical approach for a class of singular singularly perturbed systemPLOS ONE Dear Dr. Botmart, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Two reviewers have completed the review of your manuscript. Although they suggested acceptance, during our in-house check, we noticed that your manuscript contains significant references of other works by the same authors. PLOS ONE stresses that the literature review and reference list should accurately reflect the state of the field, and opposes excessive citations. Please check and revise your manuscript again following this criteria, and submit a revised version. We cannot rule out the possibility of inviting a third reviewer. Please submit your revised manuscript by Aug 14 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols. We look forward to receiving your revised manuscript. Kind regards, Hanna Landenmark Senior Editor, PLOS ONE on behalf of Chengming Huang Academic Editor, PLOS ONE Journal Requirements: Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Additional Editor Comments (if provided): [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: All comments have been addressed Reviewer #2: All comments have been addressed ******** 2. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: No ****** 5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: This paper is revised very well. All comments are addressed. It may be accepted in its current form. Reviewer #2: Now the manuscript is sutible for publication. ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0277291.r003
Revision 2
28 Jul 2022 Author Response Author Response Paper Title: A stochastic numerical approach for a class of singular singularly perturbed system by Zulqurnain Sabir, Thongchai Botmart, Muhammad Asif Zahoor Raja, Wajaree weera, Fevzi Erdoğan ID: PONE-D-21-38900R1 Journal: PLOS ONE Reviewers' comments: Reviewer #1: All comments have been addressed Authors reply Many thanks for your valuable remarks and encouraging recommendations Reviewer #2: All comments have been addressed Authors reply Many thanks for your valuable remarks and encouraging recommendations Many thanks for the Editorial Comments Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Two reviewers have completed the review of your manuscript. Although they suggested acceptance, during our in-house check, we noticed that your manuscript contains significant references of other works by the same authors. PLOS ONE stresses that the literature review and reference list should accurately reflect the state of the field, and opposes excessive citations. Please check and revise your manuscript again following this criteria, and submit a revised version. We cannot rule out the possibility of inviting a third reviewer. Authors reply First of all many thanks for both reviewer for acceptance of our manuscript in your esteemed journal after address the technical comments. We have updated the manuscript after addressing the editorial remarks regarding the reference cited in the literature review,; accordingly, after detailed, careful and critical review of the literature review for the justification of the problem statement, we have cited only those references accurately reflect/portray the state of the field. Additionally we have avoided the extensive citation of the references of the particular author as suggested for better understanding and readability. Please see the introduction and reference section of the revised manuscript. Attachments Attachment Submitted filename: Authors Response R2 28-07-2022.docx https://doi.org/10.1371/journal.pone.0277291.r004
25 Oct 2022 Decision Letter - Dragan Pamucar, Editor A stochastic numerical approach for a class of singular singularly perturbed system PONE-D-21-38900R2 Dear Dr. Botmart, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Dragan Pamucar Academic Editor PLOS ONE Additional Editor Comments (optional): Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: All comments have been addressed ******** 2. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes ****** 4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes ****** 5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: (No Response) ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No ******** https://doi.org/10.1371/journal.pone.0277291.r005

Open letter on the publication of peer review reports

PLOS recognizes the benefits of transparency in the peer review process. Therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. Reviewers remain anonymous, unless they choose to reveal their names.

We encourage other journals to join us in this initiative. We hope that our action inspires the community, including researchers, research funders, and research institutions, to recognize the benefits of published peer review reports for all parts of the research system.

Learn more at ASAPbio .