University of MazandaranCaspian Journal of Mathematical Sciences (CJMS)2676-72608220190801Adomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation.103119200710.22080/cjms.2018.14486.1346ENOlufemi ElijahIgeDepartment of Mathematics and Physics, School of Engineering science, Lappeenranta University of Technology, Lappeenranta, Finland.Razak AdekolaOderinuDepartment of Pure and Applied Mathematics, Ladoke Akintola University
of Technology, P.M.B 4000, Oyo state, Nigeria.Tarig MohyeldinElzakiMathematics Department, Faculty of Science and Arts -Alkamil, University of Jeddah, Jeddah, Saudi ArabiaJournal Article20180719Elzaki 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.http://cjms.journals.umz.ac.ir/article_2007_cad14ef1482ba482942092d05c63aa2f.pdf