A Comparison between NTDM and VIM for modified Camassa-Holm and modified Degasperis-Procesi equations

Abstract

In this paper, the Natural transform decomposition method (NTDM) which has been constructed by combining Natural transform method (NTM) and Adomian decomposition method (ADM) has been proposed. This algorithm has been applied to obtain the approximate solutions for the modified Camassa-Holm equation (mCHE) and modified Degasperis-Procesi equation (mDPE). Then, two and three dimensional surfaces have been drawn by usingWolfram Mathematica 9. A table including numerical results between approximate solutions which are obtained by using NTDM in this paper and approximate solutions which have already founded by the help of using VIM by Jafari H. et al. with the same values of parameters has been formed for mCHE and mDPE.