Abstract
The approximate solutions for the Kuramoto -Sivashinsky Equation are obtained by using the Adomian Decomposition method (ADM). The numerical example show that the approximate solution comparing with the exact solution is accurate and effective and suitable for this kind of problem. The ADM was first introduced by Adomian in the beginning of 1980's. The method is useful obtaining both a closed form and the explicit solution and numerical approximations of linear or nonlinear differential equations and it is also quite straight forward to write computer codes. This method has been applied to obtain a formal solution to a wide class of stochastic and deterministic problems in science and engineering involving algebraic, differential, integro-differential, differential delay, integral and partial differential equations. In the present study, Adomian decomposition method (ADM) has been applied to solve the Kuramoto-Sivashinsky equations. The numerical results are compared with the exact solutions. It is shown that the errors are very small. (1)
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