Numerical treatment of coupled system of fractional order partial differential equations

Volume 19, Issue 2, pp 74--85 http://dx.doi.org/10.22436/jmcs.019.02.02

Publication Date: May 01, 2019 Submission Date: September 19, 2017 Revision Date: March 31, 2019 Accteptance Date: April 06, 2019

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Authors

Amjad Ali - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan. Kamal Shah - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan. Yongjin Li - Department of Mathematics, Sun Yat-sen University, Guangzhou, P. R. China. Rahmat Ali Khan - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan.

Abstract

This manuscript is devoted to the numerical solutions of coupled system of fractional partial differential equations (FPDEs). Using Legendre polynomials for two variables, we developed some operational matrices. Based on these matrices the considered coupled system is converted to some algebraic equations which can be easily solved for the unknown coefficient matrices needed in the approximate solutions of \(u(x,t), \ v(x,t)\). The established technique is then applied to some numerical examples and the results are compared with some known wavelet methods, which demonstrate that our proposed method provides excellent solutions as compared to the other numerical methods.

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Keywords

• Shift Legendre polynomials
• coupled system of partial differential equations
• operational matrix
• algebraic equation
• numerical approximation

MSC

•  37A25
•  26A33
•  26A42

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