Novel Analytical Approach to Non-Linear Biodegradation Equations of N- Butanol in Biofilters Using Taylor's Method

Novel Analytical Approach to Non-Linear Biodegradation Equations of N- Butanol in Biofilters Using Taylor's Method | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Novel Analytical Approach to Non-Linear Biodegradation Equations of N- Butanol in Biofilters Using Taylor's Method V. Sreelatha Devi, K. Saranya, K Sudarmozhi, J. O. Akanni This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7895153/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract In the present study, an innovative analytical technique for solving nonlinear biodegradation equations of n-butanol in biofilters is introduced, which uses Taylor's method. The purpose is to produce results that are accurate and efficient. Finally, the main purpose in creating this model is to predict the n-butanol concentration level in both phases of biofilm and gas, which is important to optimize the biofiltration processes. The methodology used encompasses the application of Taylor series expansion in approximating the solutions of these complex nonlinear equations, which provide a means of an iterative solution that leads to a closed form. This method is indeed very important because it is reducing the complexity in terms of computation while providing the necessary reliable predictions, thereby making it very essential in designing and scaling biofilters. Results from this approach were found to be in very great correlation with existing numerical methods, thus validating correctness of the approach. This discussion shows the superiority of Taylor's method for non-linear biodegradation processes, but it also opens avenues into adapting this for other types of volatile organic compounds and for various biofilter configurations. The work sets the way forward for further research to be done on biofiltration methods for volatile pollutants. Diffusion limitation Biofilters Mathematical modeling Kinetics Nonlinear differential equations Biodegradation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 27 Nov, 2025 Reviews received at journal 26 Nov, 2025 Reviews received at journal 15 Nov, 2025 Reviewers agreed at journal 07 Nov, 2025 Reviewers agreed at journal 07 Nov, 2025 Reviewers agreed at journal 05 Nov, 2025 Reviewers agreed at journal 04 Nov, 2025 Reviewers invited by journal 03 Nov, 2025 Editor invited by journal 31 Oct, 2025 Editor assigned by journal 25 Oct, 2025 Submission checks completed at journal 25 Oct, 2025 First submitted to journal 18 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7895153","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":541757897,"identity":"8512bd40-cb5d-4a9e-b255-f172c41d8c58","order_by":0,"name":"V. 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The purpose is to produce results that are accurate and efficient. Finally, the main purpose in creating this model is to predict the n-butanol concentration level in both phases of biofilm and gas, which is important to optimize the biofiltration processes. The methodology used encompasses the application of Taylor series expansion in approximating the solutions of these complex nonlinear equations, which provide a means of an iterative solution that leads to a closed form. This method is indeed very important because it is reducing the complexity in terms of computation while providing the necessary reliable predictions, thereby making it very essential in designing and scaling biofilters. Results from this approach were found to be in very great correlation with existing numerical methods, thus validating correctness of the approach. This discussion shows the superiority of Taylor's method for non-linear biodegradation processes, but it also opens avenues into adapting this for other types of volatile organic compounds and for various biofilter configurations. The work sets the way forward for further research to be done on biofiltration methods for volatile pollutants.\u003c/p\u003e","manuscriptTitle":"Novel Analytical Approach to Non-Linear Biodegradation Equations of N- Butanol in Biofilters Using Taylor's Method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-13 13:45:45","doi":"10.21203/rs.3.rs-7895153/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-27T05:20:55+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-26T13:57:40+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-15T05:13:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"322382866732191510761284265822697698526","date":"2025-11-07T22:19:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"162036185026916532982332083109297265340","date":"2025-11-07T12:51:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"248018945726189721010419387604843661813","date":"2025-11-05T18:20:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3216280976392242404855809806137161563","date":"2025-11-04T11:33:28+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-03T12:39:44+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-31T14:21:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-25T05:52:31+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-25T05:51:25+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Applied Sciences","date":"2025-10-18T18:39:06+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-applied-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Applied Sciences](https://link.springer.com/journal/42452)","snPcode":"42452","submissionUrl":"https://submission.springernature.com/new-submission/42452/3","title":"Discover Applied Sciences","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7ddccc37-bf2e-4099-9d51-80e9cc603039","owner":[],"postedDate":"November 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-02-12T17:23:59+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-13 13:45:45","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7895153","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7895153","identity":"rs-7895153","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}