Analysis of the Generalized Inverse Polynomial Scheme to Initial Value Problems

Abstract

In this paper, we study the analysis of the generalized inverse polynomial scheme for the numerical solution of initial value problems of ordinary differential equation. At first, we generalize the scheme up to the fifth stage using the Binomial expansion and Taylor’s series method towards its derivation. The trend shows the generalization to the kth term. The analysis demonstrates the efficiency and the effectiveness of the generalized scheme.Keywords— Taylor’s Series, Initial Value Problem, Stability, Consistency, Convergence.