Approximate Solutions of Singularly Perturbed Nonlinear Ill-posed and Sixth-order Boussinesq Equations with Hybrid Method

Abstract

The aim of this paper is to obtain the approximate solution of singularly perturbed ill-posed and sixth-order Boussinesq equation by hybrid method (differential transform and finite difference method) as a different alternative method. Differential transform method is applied for 𝑡 −time variable and the finite difference method (central difference approach) is applied for 𝑥 −position variable. Two examples are presented to demonstrate the efficiency and reliability of the hybrid method. Numerical results are given and compared with exact solution and in literature RDTM solution. The numerical data show that hybrid method is a powerful, quite efficient and is practically well suited for solving nonlinear singular perturbed Boussinesq equations.