A second-order scheme with nonuniform time grids for the two dimensional time-fractional Zakharov-Kuznetsov equation

A second-order scheme with nonuniform time grids for the two dimensional time-fractional Zakharov-Kuznetsov equation | 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 second-order scheme with nonuniform time grids for the two dimensional time-fractional Zakharov-Kuznetsov equation Lisha Chen, Zhibo Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3977269/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 paper, we investigate the numerical method for the two dimensional time-fractional Zakharov-Kuznetsov equation. By the method of order reduction, the model is first transformed to an equivalent system. A nonlinear difference scheme is then proposed to solve the equivalent model, with min{2, rα}-th order accuracy in time and second-order accuracy in space, where α ∈ (0, 1) is the fractional order and the grading parameter r ≥ 1. The existence of the numerical solution is carefully studied by the renowned Browder fixed point theorem. With the aid of Grönwall inequality and some crucial skills, we analyze the unconditional stability and convergence of the proposed scheme based on the energy method. Finally, numerical experiments are given to illustrate the correctness of our theoretical analysis. 2010 MSC: 65M06, 65M12, 35R11 Time-fractional Zakharov-Kuznetsov equation Existence Stability Convergence Full Text Additional Declarations No competing interests reported. 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-3977269","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":274485913,"identity":"6d76a83a-7178-47e3-9126-3201d64e7e00","order_by":0,"name":"Lisha Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2UlEQVRIiWNgGAWjYDACCSB+YMCQwMDOwPggoaKGSC0JIC3MDMwGD84cI1YLA1gLm+TDFmbCOvhnNx97kFBQl8ffzP6sIrGBjYG/vTsBvyV3jqUbJBgcLpY4zGN2I3GHDIPEmbMb8GoxkMgxk0gwOJDYcJiH7UbiGTagSC4hLfnfgFrqEucfZn9WkNjGTIyWHDagFubEDYcZzBiI0iJxIw3ksMOJGw/zGEsknDnGQ9Av/DOSn0l8+FOXOO94+8OPPypq5Pjbe/FrwQA8pCkfBaNgFIyCUYAVAAChNUfboN/YiQAAAABJRU5ErkJggg==","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Lisha","middleName":"","lastName":"Chen","suffix":""},{"id":274485914,"identity":"ef407f11-d2f8-4d5f-9e6f-d273141f2d00","order_by":1,"name":"Zhibo Wang","email":"","orcid":"","institution":"Guangdong University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhibo","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-02-22 02:00:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3977269/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3977269/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51942072,"identity":"1b6f7929-c6ba-4bd4-a888-d5da0254db58","added_by":"auto","created_at":"2024-03-04 09:35:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":260074,"visible":true,"origin":"","legend":"","description":"","filename":"secondorderzk14.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3977269/v1_covered_e1a7e6ab-8089-4366-ac4a-6b980f86b0c4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A second-order scheme with nonuniform time grids for the two dimensional time-fractional Zakharov-Kuznetsov equation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Time-fractional Zakharov-Kuznetsov equation, Existence, Stability, Convergence","lastPublishedDoi":"10.21203/rs.3.rs-3977269/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3977269/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we investigate the numerical method for the two dimensional time-fractional Zakharov-Kuznetsov equation. By the method of order reduction, the model is first transformed to an equivalent system. A nonlinear difference scheme is then proposed to solve the equivalent model, with min{2, rα}-th order accuracy in time and second-order accuracy in space, where α ∈ (0, 1) is the fractional order and the grading parameter r ≥ 1. The existence of the numerical solution is carefully studied by the renowned Browder fixed point theorem. With the aid of Grönwall inequality and some crucial skills, we analyze the unconditional stability and convergence of the proposed scheme based on the energy method. 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