Numerical solution of hirota-satsuma couple Kdv and a coupled MKdv equation by means of homotopy analysis method

In this paper, the numerical solution of systems of Hirota-Satsuma coupled Kdv and a coupled MKdv Equation by means of Homotopy Analysis Method (HAM) are presented. The HAM can extremely minimize the volume of computations with respect to traditional techniques and yields the analytical solution of the desired problem in the form of a rapidly convergent series with easily computable components. To illustrate the ability and flexibility of the method some examples are provided. A comparison was also made between HAM and Adomian Decomposition Method (ADM). The results reveal that the method is very effective and simple. © IDOSI Publications, 2011