Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

Abstract

<p class="Char">In this paper, the modified Adomian decomposition method (MADM) is usedto solve different types of differential equations, one of the numerical analysis methods for solving non linear partial differential equations (Drinfeld–Sokolov–Wilson system) and short (DSWS) that occur in shallow water flows. A Genetic Algorithm was used to find the optimal value for the parameter (a). We numerically solved the system (DSWS) and compared the result to the exact solution. When the value of it is low and close to zero, the MADM provides an excellent approximation to the exact solution. As well as the lower value of leads to the numerical algorithm of (MADM) approaching the real solution. Finally, found the optimal value when a=-10 by using the Genetic Algorithm (G-MADM). All the computations were carried out with the aid of Maple 18 and Matlab to find the parameter value (a) by using the genetic algorithm as well as to figures drawing. The errors in this paper resulted from cut errors and mean square errors.</p>

New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

“…Günay et al [10] derived solitary wave solutions to the DSS using the generalized exponential rational function method. Salim et al [11] solved the Drinfeld-Sokolov-Wilson system numerically using the modified Adomian decomposition method. Alam et al [12] established some exact solutions of the Drinfeld-Sokolov-Wilson equation with S(ξ)-expansion method.…”