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

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• 作者：Eid H Doha (6)
  Ali H Bhrawy (7) (8)
  Dumitru Baleanu (10) (11) (9)
  Samer S Ezz-Eldien (12)
  
  6. Department of Mathematics ; Faculty of Science ; Cairo University ; Giza ; Egypt
  7. Department of Mathematics ; Faculty of Science ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  8. Department of Mathematics ; Faculty of Science ; Beni-Suef University ; Beni-Suef ; Egypt
  10. Department of Mathematics and Computer Sciences ; Faculty of Arts and Sciences ; Cankaya University ; Ankara ; Turkey
  11. Institute of Space Sciences ; Magurele-Bucharest ; Romania
  9. Department of Chemical and Materials Engineering ; Faculty of Engineering ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  12. Department of Basic Science ; Institute of Information Technology ; Modern Academy ; Cairo ; Egypt
  
• 关键词：multi ; term fractional differential equations ; fractional diffusion equations ; tau method ; shifted Jacobi polynomials ; operational matrix ; Caputo derivative
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：460 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

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.