Numerical approach for brain tumor growth model using higher order compact finite difference scheme

Numerical approach for brain tumor growth model using higher order compact finite difference scheme | 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 Numerical approach for brain tumor growth model using higher order compact finite difference scheme Hirak Jyoti Das, Shuvam Sen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3972812/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 focus on analyzing the reaction-diffusion model applied to brain gliomas, incorporating two distinct types of growth functions. To gain a comprehensive understanding, we extend our analysis to different types of tissue environments. We explore scenarios where the diffusion coefficient remains constant, reflecting a homogeneous tissue environment. Additionally, we investigate cases where the diffusion coefficient becomes spatially variable, introducing heterogeneity into the model. This spatial variability accounts for the varying properties of different regions within the brain. Subsequently, we extend our investigation to heterogeneous tissue environments in $2$-dimensions. Our analysis of simulation results reveals differences in growth patterns based on the parameters utilized. Brain glioma growth Crank-Nicolson method reaction-diffusion model diffusion Proliferation 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-3972812","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":274075266,"identity":"56ccbd9b-35a1-4a46-989c-8ac67f2aa458","order_by":0,"name":"Hirak Jyoti Das","email":"","orcid":"","institution":"Tezpur University","correspondingAuthor":false,"prefix":"","firstName":"Hirak","middleName":"Jyoti","lastName":"Das","suffix":""},{"id":274075267,"identity":"5ec70900-63b9-4f27-a9c7-c3d42bf67c9a","order_by":1,"name":"Shuvam Sen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDACCTBpgyzE2ECMljQJuAAPkVoOI2shAORn95hJ/Mw5X8fPf8aA4eOeO3L2DMxtD/BpMbhzxkyyd9ttCcmGMwaMM549MwY6rN0ArxaJHGMDXqAWg4M9Bsw8Bw4n9jAwtkng0yI/I8fY8O+2cxL2h3kMmP8cOFxPUAvDjRzDx7zbDkgYsAG1MBw4nMBDSIvBjbTCx7LbkiVnnGErONhz4LBhz2GCDkvecPDtNjt+/v7DGx/8OHBYnr29/Rl+hyGDA2CSmWj1o2AUjIJRMApwAQDrSEXEiU4KSAAAAABJRU5ErkJggg==","orcid":"","institution":"Tezpur University","correspondingAuthor":true,"prefix":"","firstName":"Shuvam","middleName":"","lastName":"Sen","suffix":""}],"badges":[],"createdAt":"2024-02-20 12:50:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3972812/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3972812/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52997406,"identity":"dc319ae1-4512-47e1-ae6a-e38d9ee1290b","added_by":"auto","created_at":"2024-03-19 13:42:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7277198,"visible":true,"origin":"","legend":"","description":"","filename":"Numericalsolutionofreactiondiffusionmodel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3972812/v1_covered_f1ed3365-29e1-4a43-bfad-58fbc991f63d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical approach for brain tumor growth model using higher order compact finite difference scheme","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":"Brain glioma growth, Crank-Nicolson method, reaction-diffusion model, diffusion, Proliferation","lastPublishedDoi":"10.21203/rs.3.rs-3972812/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3972812/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this article, we focus on analyzing the reaction-diffusion model applied to brain gliomas, incorporating two distinct types of growth functions. 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