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

## Keywords

Shifted Chebyshev polynomials
Variable order fractional partial differential equations
Error correction
Variable order differential operator matrix

## How to Cite

Hong Xia Sun, Xing Jun Zhang, Yi-Ming Chen, & Lei Wang. (2020). A Numerical Method with Shifted Chebyshev Polynomials for a Set of Variable Order Fractional Partial Differential Equations. Journal of Advances in Applied &Amp; Computational Mathematics, 7, 57–69. https://doi.org/10.15377/2409-5761.2020.07.8

## 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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