Adomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation

Ige, Olufemi Elijah; Oderinu, Razak Adekola; Elzaki, Tarig Mohyeldin

doi:10.22080/cjms.2018.14486.1346

Adomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation

Document Type : Research Articles

Authors

¹ Department of Mathematics and Physics, School of Engineering science, Lappeenranta University of Technology, Lappeenranta, Finland.

² Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, P.M.B 4000, Oyo state, Nigeria.

³ Mathematics Department, Faculty of Science and Arts -Alkamil, University of Jeddah, Jeddah, Saudi Arabia

10.22080/cjms.2018.14486.1346

Abstract

Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle nonlinear functions on its own. In all the three problems considered, the series solutions obtained converges to the exact solutions. Three dimensional graphs were also plotted to give the shape of the solutions of some KdV equations considered. Hence, Elzaki transform and Adomian polynomial together gives a very powerful and ffective method for solving nonlinear partial differential equations.

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