Hybrid shifted polynomial scheme for the approximate solution of a class of nonlinear partial differential equations

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dc.contributor.authorOnanaye, Adeniyi Samson
dc.date.accessioned2025-05-08T13:27:43Z
dc.date.available2025-05-08T13:27:43Z
dc.date.issued2024
dc.description.abstractThis research focuses on the development of a streamlined numerical technique founded on the hybridization of two shifted polynomial basis functions to address a specific category of nonlinear Partial Differential Equations. Within this approach, a solution based on power series is employed, utilizing Chebyshev and Legendre shifted polynomials to meet the specific conditions of the Partial Differential Equation. Plugging the candidate solution series into the provided Partial Differential Equation, and employing suitable points of collocation, a linear system of algebraic equations with unspecified hybridization coefficients was obtained and numerically solved by Gaussian elimination. Furthermore, different discretization patterns were examined to comprehend how the outcomes vary with alterations in the placement of the collocation points within the domain. Two instances were examined using the numerical method to determine the method’s efficiency in terms of its reliability, effectiveness, and accuracy. The results obtained were benchmarked and validated with existing results in the literature. However, the combination of the two shifted orthogonal polynomials (Chebyshev and Legendre) greatly improved performance past that in prior literature.
dc.identifier.urihttps://repository.run.edu.ng/handle/123456789/4427
dc.language.isoen
dc.publisherSongklanakarin J. Sci. Technol
dc.titleHybrid shifted polynomial scheme for the approximate solution of a class of nonlinear partial differential equations
dc.typeArticle
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