Hybrid shifted polynomial scheme for the approximate solution of a class of nonlinear partial differential equations
This 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, utili...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Prince of Songkla University
2024-08-01
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| Series: | Songklanakarin Journal of Science and Technology (SJST) |
| Subjects: | |
| Online Access: | https://sjst.psu.ac.th/journal/46-4/3.pdf |
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| Summary: | This 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. |
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| ISSN: | 0125-3395 |