Approximate analytical solutions of singularly perturbed fourth order boundary value problems using differential transform method

Abstract

In this paper, a reliable algorithm is presented to develop approximate analytical solutions of fourth order singularly perturbed two-point boundary value problems in which the highest order derivative is multiplied by a small parameter. In this method, first the given problem is transformed into a system of two second order ODEs, with suitable boundary conditions and a zeroth-order asymptotic approximate solution of the transformed system is constructed. Then, the reduced terminal value system is solved analytically using the differential transform method. Some illustrating examples are solved and the results are compared with the exact solutions to demonstrate the accuracy and the efficiency of the method. It is observed that the present method approximates the exact solution very well not only in the boundary layer, but also away from the layer. © 2013 .