Approximate Solutions of the Swift-Hohenberg Equation with Dispersion

Abstract

In this paper, the initial and boundary value problems for the Swift-Hohenberg equation as over the finite spatial interval \(x \in [0,l]\) and finite time interval \(t \in [0,t^*]\) are considered. Approximate solutions for the initial and boundary value problems are obtained via the differential transform method and reduced differential transform method. Finally, several numerical examples are presented in order to demonstrate the effectivity of the methods and clarify the influence of the parameters on the solution.