Numerical simulation of the nonlinear coupled jaulent-miodek equation by elzaki transform-adomian polynomial method

Abstract

The Elzaki transform which is an integral transform used to obtain solutions of linear differential equations is coupled with Adomian polynomial to solve nonlinear coupled Jaulent-Miodek (JM) equation. The Adomian polynomial is used to linearise the nonlinear functions in the partial differential equation before the scheme of the Elzaki transform was used to iteratively generate each term of the series solution. The solutions obtained were compared with the exact solutions and were found to give a very small error, the graphical representation of the solutions which give the shape of the solitons also agree with that of the Adomian decomposition method when a comparison is made. The method is powerful and effective as it does not involve large computer memory and does not involve discretizing the independent variables to achieve the required solution.