A NEW APPROACH FOR FINDING CLOSED FORM SOLUTION OF NTH ORDER INITIAL VALUE PROBLEMS

Abstract

This article proposes a new technique for finding exact solution of N -th order, linear, nonlinear and stiff initial value problems. By recasting the problem as a system of constant coefficient polynomial ordinary differential equation, the coefficients of the power series solution is computed iteratively. The closed form solution is obtained from the truncated series solution by applying Padé and Laplace-Padé post-processing. The application of the method to various problems considered elucidated the simplicity and high accuracy of the proposed approach.