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

• 作者: Fuqiang Zhao Jiaquan Xie Jun Zhang Zhibin Yao
• 来源期刊: 工程与科学中的计算机建模(英文)
• 学科: 数学
• 关键词: Three-variable shifted Jacobi polynomials multi-term FRACTIONAL-ORDER PDES VARIABLE coefficients numerical solution convergence analysis
• 年，卷（期）: 2018,（4）
• 页码范围: 67-84
• 页数: 18页
• 分类号: O17

摘要

In this paper,the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional 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 threevariable 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.