Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM

In this study, generalized Hirota–Satsuma coupled KdV equation is solved using by two recent semi-analytic methods, differential transform method (DTM) and reduced form of differential transformation method (so called RDTM). The concepts of DTM and RDTM is briefly introduced, and their application for generalized Hirota–Satsuma coupled KdV equation is studied. The results obtained employing DTM and RDTM are compared with together and exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by classic DTM. The numerical results reveal that the RDTM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the RDTM can be found widely applicable in engineering.

► Differential transform method (DTM) and their new reduced form, co called RDTM, are introduced.
► To compare of these methods, we considered the generalized Hirota-Satsuma coupled KdV equation.
► Both DTM and RDTM are applied to obtain numerical solution of generalized Hirota-Satsuma coupled KdV equation.
► As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM.