A Note on Solving Nonlinear Differential Equations Using Modified Laplace Decomposition Method - Mulatu, Lemma,; Wilkins, Amar; Chowdhury, Abhinandan; Franklin, Crystal (IJRDO -JOURNAL OF MATHEMATICS, 2019)
In the field of Applied Mathematics, physics, and engineering, to explain phenomena occur- ring in these fields, models are developed in the form of differential equations. Many of these phenomena are typically represented as nonlinear differential equations. While there exist a hand- ful of analytical methods to solve some regular problems, often an analytical solution turns out to be quite difficult to attain using traditional methods. Therefore the objective is to explore a numerical method or a semi-analytical method that yields the best approximation. In this paper, we investigate a consistent modification of Laplace decomposition method using Adomian poly- nomials to solve nonlinear ordinary and partial differential equations. The method is introduced and to further demonstrate its effectiveness, it is applied to solve three differential equations where nonlinearity appears in different forms.