文章基本信息

标题：The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation
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作者：Eid H Doha ; Ali H Bhrawy ; Dumitru Baleanu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：231
DOI：10.1186/1687-1847-2014-231
语种：English
出版社：Hindawi Publishing Corporation
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.
关键词：multi-term fractional differential equations ; fractional diffusion equations ; tau method ; shifted Jacobi polynomials ; operational matrix ; Caputo derivative