Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Shifted Chebyshev Spectral Method for Two-Dimensional Space-Time Fractional Partial Differential Equations

Version 1 : Received: 9 May 2022 / Approved: 10 May 2022 / Online: 10 May 2022 (10:19:34 CEST)

How to cite: Oloniiju, S.; Nkomo, N.; Goqo, S.; Sibanda, P. Shifted Chebyshev Spectral Method for Two-Dimensional Space-Time Fractional Partial Differential Equations. Preprints 2022, 2022050138 (doi: 10.20944/preprints202205.0138.v1). Oloniiju, S.; Nkomo, N.; Goqo, S.; Sibanda, P. Shifted Chebyshev Spectral Method for Two-Dimensional Space-Time Fractional Partial Differential Equations. Preprints 2022, 2022050138 (doi: 10.20944/preprints202205.0138.v1).

Abstract

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

Keywords

Shifted Chebyshev polynomials; Chebyshev-Gauss-Lobatto quadrature; space-time FPDE

Subject

MATHEMATICS & COMPUTER SCIENCE, Numerical Analysis & Optimization

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