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

Muhammad Ikhlaq Chohan, Kamal Shah

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.

Keywords

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

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