Numerical Approximation of Oscillatory Initial Value Problem Using the Homotopy Analysis Algorithm

Abstract

In this paper, we present numerical approximation for oscillatory initial value problems (IVPs) using the homotopy analysis algorithm. The convergence of the method is discussed and numerical experiments are presented to illustrate the computational effectiveness of the algorithm. The results obtained are in good agreement with the exact solutions and Adomian decomposition method (ADM). These results show that the algorithm introduced here is accurate and easy to apply without linearization.