On a Computational Method for Non-integer Order Partial Differential Equations in Two Dimensions

Authors

  • Muhammad Ikhlaq Chohan Department of Business Administration and Accounting Al Buraimi University College, Al-Buraimi Sultanate of Oman
  • Kamal Shah Department of Mathematics University of Malakand

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i1.3377

Keywords:

Jacobi polynomials, Different classes of partial differential equations, Operational matrix, Algebraic equation, Numerical solution.

Abstract

This manuscript is concerning to investigate numerical solutions for different classes
including parabolic, elliptic and hyperbolic partial differential equations of arbitrary order(PDEs). The proposed technique depends on some operational matrices of fractional order differentiation and integration. To compute the mentioned operational matrices, we apply shifted Jacobi polynomials in two dimension. Thank to these matrices, we convert the (PDE) under consideration to an algebraic equation which is can be easily solved for unknown coefficient matrix required for the numerical solution. The proposed method is very efficient and need no discretization of the data for the proposed (PDE). The approximate solution obtain via this method is highly accurate and the computation is easy. The proposed method is supported by solving various examples from well known articles.

Author Biography

Muhammad Ikhlaq Chohan, Department of Business Administration and Accounting Al Buraimi University College, Al-Buraimi Sultanate of Oman

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How to Cite

Chohan, M. I., & Shah, K. (2019). On a Computational Method for Non-integer Order Partial Differential Equations in Two Dimensions. European Journal of Pure and Applied Mathematics, 12(1), 39–57. https://doi.org/10.29020/nybg.ejpam.v12i1.3377