The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation

Advances in Difference Equations

Samer S Ezz-Eldien¹  Dumitru Baleanu²  Eid H Doha³  Ali H Bhrawy⁴ 

[1] Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt;Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: multi-term fractional differential equations;    fractional diffusion equations;    tau method;    shifted Jacobi polynomials;    operational matrix;    Caputo derivative;   

DOI  :  10.1186/1687-1847-2014-231

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, an accurate and efficient numerical method is presented for solving the space-fractional order diffusion equation (SFDE). Jacobi polynomials are used to approximate the solution of the equation as a base of the tau spectral method which is based on the Jacobi operational matrices of fractional derivative and integration. The main advantage of this method is based upon reducing the nonlinear partial differential equation into a system of algebraic equations in the expansion coefficient of the solution. In order to test the accuracy and efficiency of our method, the solutions of the examples presented are introduced in the form of tables to make a comparison with those obtained by other methods and with the exact solutions easy.

【 授权许可】

CC BY