Modal spectral Tchebyshev Petrov–Galerkin stratagem for the time-fractional nonlinear Burgers’ equation
Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for handling the nonlinear time-fractional Burger-type partial differential equation in the Caputo sense. The process reduces the pr...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Ferdowsi University of Mashhad
2024-01-01
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Series: | Iranian Journal of Numerical Analysis and Optimization |
Subjects: | |
Online Access: | https://ijnao.um.ac.ir/article_44440_66f86391a179ed34bc141dfbaf0d1f6a.pdf |
Summary: | Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for handling the nonlinear time-fractional Burger-type partial differential equation in the Caputo sense. The process reduces the problem to a nonlinear system of algebraic equations. Solving this alge-braic equation system will yield the approximate solution’s unknown coef-ficients. Many relevant properties of Chebyshev polynomials are reported, some connection and linearization formulas are reported and proved, and all elements of the obtained matrices are evaluated neatly. Also, conver-gence and error analyses are established. Various illustrative examples demonstrate the applicability and accuracy of the proposed method and depict the absolute and estimated error figures. Besides, the current ap-proach’s high efficiency is proved by comparing it with other techniques in the literature. |
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ISSN: | 2423-6977 2423-6969 |