Petrov-Galerkin Lucas Polynomials Procedure for the Time-Fractional Diffusion Equation

Authors

DOI:

https://doi.org/10.37256/cm.4220232420

Keywords:

time-fractional diffusion equation, Lucas polynomials, Lucas number, golden ratio, Petrov-Galerkin method, Convergence analysis

Abstract

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the spatial homogenous boundary conditions. This basis is then used to solve the time-fractional diffusion equation spectrally. The elements of all spectral matrices are explicitly obtained in terms of the Gauss hypergeometric function. The convergence and error analysis of the proposed Lucas expansion is studied. Numerical results indicate the high accuracy and applicability of the suggested algorithm.

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Published

2023-04-08

How to Cite

1.
Youssri YH, Atta AG. Petrov-Galerkin Lucas Polynomials Procedure for the Time-Fractional Diffusion Equation. Contemp. Math. [Internet]. 2023 Apr. 8 [cited 2024 Jun. 19];4(2):230-48. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2420