Abstract
In this study, high accurate numerical solutions of the modified Korteweg-de Vries equation via contribution of two effective methods and efficient linearizing technique are obtained. In order to observe the performance of the present approximation, five famous applications will be handled. To see the position of the new method in the scientific literature, all numerical results obtained by using the same parameters with earlier applications and compared with each other. Furthermore, to display the numerical behaviour of the shallow water waves, all of the applications are illustrated in detail and given in 2D and 3D. Numerical results show that present algorithm will be useful for the other nonlinear scientific problems.
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