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    Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients

    Jiaquan Xie1,3,*, Fuqiang Zhao1,3, Zhibin Yao1,3, Jun Zhang1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.1, pp. 67-84, 2018, DOI:10.3970/cmes.2018.115.067

    Abstract In this paper, the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of three-dimensional multi-term fractional-order PDEs with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by three-variable shifted Jacobi polynomials are compared with the exact solutions. Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm. Lastly, several numerical examples are presented… More >

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