A Note on Solving Nonlinear Differential Equations Using Modified Laplace Decomposition Method

  • Lemma, Mulatu
  • Amar Wilkins
  • Abhinandan Chowdhury
  • Crystal Franklin
Keywords: Nonlinear PDE, Modified Laplace Decomposition Method

Abstract

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.

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Author Biography

Amar Wilkins

Department of Mathematics

Savannah State University

 

                                                                                   USA

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Published
2019-01-29
How to Cite
Mulatu, L., Wilkins, A., Chowdhury, A., & Franklin, C. (2019). A Note on Solving Nonlinear Differential Equations Using Modified Laplace Decomposition Method. IJRDO - Journal of Mathematics (ISSN: 2455-9210), 5(1), 12-19. Retrieved from https://ijrdo.org/index.php/m/article/view/2509

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