Solution of time‐fractional generalized Hirota‐Satsuma coupled KdV equation by generalised differential transformation method

Abstract

Purpose

In this article, the aim is to obtain an approximate analytical solution of time‐fraction generalized Hirota‐Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions.

Design/methodology/approach

Two dimensional differential transformation method (DTM) is used.

Findings

In this paper, the fractional differential transformation method is implemented to the solution of time‐fraction generalized generalized Hirota‐Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial.

Originality/value

This is an original work in which the results indicate that the method is powerful and significant for solving time‐fraction generalized generalized Hirota‐Satsuma coupled KDV type differential equations.

Citation

Merdan, M., Gökdoğan, A., Yildirim, A. and Tauseef Mohyud‐Din, S. (2013), "Solution of time‐fractional generalized Hirota‐Satsuma coupled KdV equation by generalised differential transformation method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 5, pp. 927-940. https://doi.org/10.1108/HFF-09-2011-0188