A fast Chebyshev wavelet numerical method for the solution of the Advection partial differential equations

A fast Chebyshev wavelet numerical method for the solution of the Advection partial differential equations | 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 A fast Chebyshev wavelet numerical method for the solution of the Advection partial differential equations Vivek ., Manoj Kumar, Suyash Narayan Mishra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2987954/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this article, we present a computationally efficient technique based on the method of Chebyshev wavelets and collocation technique for the solution of linear and nonlinear the Advection partial differential equations. We transform these problems into a system of algebraic equations using truncated Chebyshev wavelet expansions and then simplified using a suitable method. The suggested Chebyshev wavelet approach is worked out for the convergence analysis it is demonstrated that the estimation of a function using Chebyshev wavelets converges uniformly to itself. It is also anticipated that the proposed approach would be more efficient and suitable for solving a variety of nonlinear partial differential equations that occur in science and engineering. Examples are given to show how the suggested wavelet method provides enhanced accuracy for a wide range of problems. Taylor wavelet Collocation points Advection equation Newton iterative method MATLAB Full Text Additional Declarations No competing interests reported. Supplementary Files fig.eps snapacite.bst snaps.bst snarticle.tex snbasic.bst snbibliography.bib snchicago.bst snjnl.cls snmathphys.bst snsamplebib.tex snstandardnature.bst snvancouver.bst Cite Share Download PDF Status: Posted Version 1 posted 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-2987954","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":204856571,"identity":"410dddbd-99ac-4c19-b71e-c36c83d9c8b4","order_by":0,"name":"Vivek .","email":"","orcid":"","institution":"Institute of Engineering and Technology, Lucknow","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Vivek","middleName":"","lastName":".","suffix":""},{"id":204856572,"identity":"0d6f0f6d-6c6a-4374-9023-510eee56435a","order_by":1,"name":"Manoj 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