Adomian Polynomial and Elzaki Transform Method for Solving Sine-Gordon Equations

Elzaki transform is combined with Adomian polynomial to obtain an approximate analytical solutions of non-linear Sine Gordon equations. The necessity of Adomian polynomial is to linearise the nonlinear function(s) that is present in any given differential equation(s) because Elzaki transform, like o...

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Bibliographic Details
Published inIAENG international journal of applied mathematics Vol. 49; no. 3; pp. 1 - 7
Main Authors Ige, Olufemi Elijah, Oderinu, Razaq Adekola, Elzaki, Tarig M
Format Journal Article
LanguageEnglish
Published Hong Kong International Association of Engineers 01.08.2019
Subjects
Exact solutions
Integral transforms
Mathematical analysis
Nonlinear analysis
Nonlinear differential equations
Nonlinear equations
Polynomials
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Summary:Elzaki transform is combined with Adomian polynomial to obtain an approximate analytical solutions of non-linear Sine Gordon equations. The necessity of Adomian polynomial is to linearise the nonlinear function(s) that is present in any given differential equation(s) because Elzaki transform, like other integral transforms, cannot be used to solve nonlinear differential equation independently. The approximate analytical solutions are presented in series form. In order to investigate the performance of the method, two single nonlinear Sine Gordon equations and one coupled Sine Gordon equation were considered in this paper. The method is very powerful because one of the problems considered converges to the exact solution and this shows the effectiveness of this method in solving nonlinear Sine Gordon equations.
ISSN:1992-9978
1992-9986