Modal spectral Tchebyshev Petrov-Galerkin stratagem for the time-fractional nonlinear Burgers' equation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 آبان 1402

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.83389.1292

نویسندگان

Youssri Hassan Youssri^{* 1}؛ Ahmed Gamal Atta²

¹Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

²Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt

چکیده

Herein, we construct an explicit modal numerical solver based on the spectral Petrov-Galerkin method via a specific combination of shifted Chebyshev 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 algebraic equation system will yield the approximate solution's unknown coefficients. Many relevant properties of Chebyshev polynomials were reported, some connection and linearization formulae were reported and proved, and all elements of the obtained matrices were evaluated neatly. Also, convergence and error analyses were established. Various illustrative examples demonstrate the applicability and accuracy of the proposed method and depict the absolute and estimated error figures. Besides, the current approach's high efficiency is proved by comparing it with other techniques in the literature.

کلیدواژه‌ها

Time fractional Burgers' equation؛ Chebyshev polynomials؛ Petrov-Galerkin method؛ Convergence analysis