Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomian Polynomial

Mousumi Datta^1, , Umme Habiba¹ and Md. Babul Hossain¹

¹Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail, Bangladesh

Cite this paper:
Mousumi Datta, Umme Habiba and Md. Babul Hossain. Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomian Polynomial. International Journal of Partial Differential Equations and Applications. 2020; 8(1):6-12. doi: 10.12691/ijpdea-8-1-2

Abstract

In this paper we apply a new method, named Elzaki Substitution Method to solve nonlinear homogeneous and nonhomogeneous partial differential equations with mixed partial derivatives, which is based on Elzaki Transform. The proposed method introduces also Adomian polynomials and the nonlinear terms can be handled by the use of this polynomials. The proposed method worked perfectly to find the exact solutions of partial equations with mixed partial derivatives without any need of linearization or discretization in comparison with other methods such as Method of Separation of Variables (MSV) and Variation Iteration Method (VIM). Some illustrative examples are given to demonstrate the applicability and efficiency of proposed method.

Keywords:
Partial Differential Equations Exact Solution Mixed Partial Derivatives Elzaki Transform Elzaki Substitution Method Adomian polynomial

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