TY - EJOU
AU - Xie, Jiaquan
AU - Zhao, Fuqiang
AU - Yao, Zhibin
AU - Zhang, Jun
TI - Three-Variable Shifted Jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients
T2 - Computer Modeling in Engineering \& Sciences
PY - 2018
VL - 115
IS - 1
SN - 1526-1506
AB - 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 to test the superiority and efficiency of the proposed method.
KW - Three-variable shifted Jacobi polynomials
KW - multi-term fractional-order PDEs
KW - variable coefficients
KW - numerical solution
KW - convergence analysis
DO - 10.3970/cmes.2018.115.067