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


  • Xing Jun Zhang School of Sciences, Yanshan University, Qinhuangdao, Hebei, China
  • Hong Xia Sun School of Sciences, Yanshan University, Qinhuangdao, Hebei, China
  • Yi-Ming Chen School of Sciences, Yanshan University, Qinhuangdao, Hebei, China
  • Lei Wang School of Sciences, Yanshan University, Qinhuangdao, Hebei, China




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


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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How to Cite

Zhang, X. J. ., Xia Sun, H. ., Chen, Y.-M. ., & Wang, L. . (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(1), 57–69. https://doi.org/10.15377/2409-5761.2020.07.8