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


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 & Computational Mathematics, 7, 57–69. https://doi.org/10.15377/2409-5761.2020.07.8


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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