An Elzaki Transform Decomposition Algorithm Applied to a Class of Non-Linear Differential Equations

Abstract

Another version of the classic Sumudu Transform called the Elzaki Transform, was put forward as closely related to the Laplace Transform. In the following paper, the Elzaki Transform Algorithm, which has been built on the Decomposition Method, is presented to be applied to find approximate solution of a class of non-linear, initial value problems. This method gives an approximate solution in a Convergent-Series form with easily computable components necessitating no linearization or a low perturbation criterion. The most important part of this paper is the error analysis conducted between exact solutions and pade approximate solutions; it proves that our approximate solutions narrow in rapidly to the exact solutions. Moreover, as we will discuss after the results are resented, this algorithm can also be applicable to more general classes of linear and nonlinear differential equations.

Key Words: Elzaki Transform, Adomian Decomposition Method; Nonlinear Differential Equation, Series Solution, Convergence.