The Aboodh reduced differential transform method for the Hirota-Satsuma coupled KDV and MKDV equations

Abstract

This paper presents the validity and efficiency of the coupled Aboodh and Reduced Differential Transform Methods (ABRDTM). This method has been used in solving the coupled mKdV and KdV equations involving two different types of initial conditions. The Reduced Differential Transform Method which is a modified form of differential transform method (DTM) and emanated from the Taylors expansion is incorporated into the scheme of the Aboodh transform method and calculated in an iterative procedure which converged quickly to a closed form solution. In this work, the examples illustrated showed that the scheme provides a series of function which converged to the analytical solutions of the system earlier mentioned.