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A Numerical Method with Shifted Chebyshev Polynomials for a Set of Variable Order Fractional Partial Differential Equations

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Title: A Numerical Method with Shifted Chebyshev Polynomials for a Set of Variable Order Fractional Partial Differential Equations

Authors: Hong Xia Sun, Xing Jun Zhang, Yi-Ming Chen, Lei Wang

Journal: Journal of advances in applied & computational mathematics

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Year: 2020

Volume: 7

Language: en

DOI: 10.15377/2409-5761.2020.07.8

Keywords: Error CorrectionShifted Chebyshev polynomialsVariable order fractional partial differential equationsVariable order differential operator matrix

Categories
Polynomials (22) Numerical Analysis (431) Differential Equations (206) Mathematics (5170) Fractional Calculus (72)

Abstract

In this paper, a high-efficiency numerical algorithm based on shifted Chebyshev polynomials is given to solve a set of variable-order fractional partial differential equations. First, we structure the differential operator matrix of the shifted Chebyshev polynomials. Then, we transform the problem into solving a set of linear algebraic equations to obtain the numerical solution. Moreover, a step of error correction is given. Finally, numerical examples are given to show the effectiveness and practicability of the proposed method.

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