Scheme Based Comparison for Benjamin-Bona-Mahony-BurgersEquation Governing Flood Predictions

Scheme Based Comparison for Benjamin-Bona-Mahony-BurgersEquation Governing Flood Predictions | 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 Scheme Based Comparison for Benjamin-Bona-Mahony-BurgersEquation Governing Flood Predictions Priyanka Yadav, Aditi Singh, Sumita Dahiya This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8075200/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 This manuscript aims to assess the applicability of a variant of the cubic B–spline collocation method to handlenonlinear partial differential equations of higher orders, usually more than two. For this purpose, two differentversions of the Benjamin–Bona–Mahony–Burgers equation, which governs flood prediction, are taken into accountand simulated numerically using the proposed method. The time derivatives in the governing equation areapproximated by employing the Crank–Nicolson scheme, while the improvised cubic B–spline collocation approach(ICBCA) is designed to approximate the spatial derivatives. The nonlinearity in the governing equation has beendealt with using the Rubin–Graves method. The techniques that are employed ensure that the resulting matrixremains diagonally dominant and the boundary conditions are implemented with ease. The von Neumann analysistechnique is used to establish stability. The conserved quantities are calculated to verify that the conservationlaws are maintained as expected from the theory. The numerical results confirm the accuracy and effectivenessof the approach for both versions of the BBM–Burgers equation and confirm its suitability for solving nonlinearproblems of higher order in both space and time. Flood prediction Benjamin–Bona–Mahony–Burgers equation improvised cubic B–spline collocation approach Crank–Nicolson scheme Rubin–Graves method von Neumann analysis error norms L∞ and L2 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. 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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-8075200","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":542544824,"identity":"f770fe43-d400-473b-b383-13ab1bf8bd3c","order_by":0,"name":"Priyanka Yadav","email":"","orcid":"","institution":"Netaji Subhas University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Priyanka","middleName":"","lastName":"Yadav","suffix":""},{"id":542544825,"identity":"55a9d64d-b49d-4970-9760-c07d9c9cacf3","order_by":1,"name":"Aditi Singh","email":"","orcid":"","institution":"Dr. Bhim Rao Ambedkar 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For this purpose, two differentversions of the Benjamin–Bona–Mahony–Burgers equation, which governs flood prediction, are taken into accountand simulated numerically using the proposed method. The time derivatives in the governing equation areapproximated by employing the Crank–Nicolson scheme, while the improvised cubic B–spline collocation approach(ICBCA) is designed to approximate the spatial derivatives. The nonlinearity in the governing equation has beendealt with using the Rubin–Graves method. The techniques that are employed ensure that the resulting matrixremains diagonally dominant and the boundary conditions are implemented with ease. The von Neumann analysistechnique is used to establish stability. The conserved quantities are calculated to verify that the conservationlaws are maintained as expected from the theory. 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