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

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