Spectral tau solution of the linearized time-fractional KdV-Type equations

AIMS Mathematics

article

Waleed Mohamed Abd-Elhameed¹  Youssri Hassan Youssri² 

[1] Department of Mathematics, College of Science, University of Jeddah;Department of Mathematics, Faculty of Science, Cairo University

关键词: tau method;    second-kind Chebyshev polynomials;    KdV equations;    fractional differential equations;    convergence analysis;   

DOI  :  10.3934/math.2022830

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

The principal objective of the current paper is to propose a numerical algorithm for treating the linearized time-fractional KdV equation based on selecting two different sets of basis functions. The members of the first set are selected to be suitable combinations of the Chebyshev polynomials of the second kind and also to be compatible with the governing boundary conditions of the problem, while the members of the second set are selected to be the shifted second-kind Chebyshev polynomials. After expressing the approximate solutions as a double expansion of the two selected basis functions, the spectral tau method is applied to convert the equation with its underlying conditions into a linear system of algebraic equations that can be treated numerically with suitable standard procedures. The convergence analysis of the double series solution is carefully tested. Some numerical examples accompanied with comparisons with some other methods in the literature are displayed aiming to demonstrate the applicability and accuracy of the presented algorithm.

【 授权许可】

CC BY