Approximate analytical solution of nonlinear differential equations using Elzaki transform : Case study: Kortewed-de Vries (KdV) Equations
Ige, Olufemi Elijah (2018)
Ige, Olufemi Elijah
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The combination of Elzaki transform and Adomian was used to obtain the approximate analytical solutions of KdV equations in this research work. In total, three third order KdV equations and two fifth order KdV equations were considered. Elzaki transform method was applied to obtain the approximate analytical solutions of all the aforementioned equations. Adomian polynomial was introduce as essential tool to linearize all the associated nonlinear terms in the equations since Elzaki transform cannot handle nonlinear terms. All the problem considered yield exact solutions with few iterations. The solutions obtained were compared with the solutions obtained by other existing method (Homotopy perturbation transform method and Laplace decomposition method for third and fifth order KdV equation respectively). The solutions obtained with the Elzaki transform method happen to be the same as the solutions obtained by using Homotopy perturbation transform method and Laplace decomposition method. All the problems considered show that the Elzaki transform method and Adomian polynomial are very powerful integral transform methods in solving some nonlinear Equations like KdV equations. In addition we obtain the numerical solution of Kdv equation using finite difference method and we compare the numerical solution to the analytical solution of KdV equation both are almost the same. The finite difference method of KdV equation was implemented in Matlab.