Improved Predictor-corrector Method for the Initial-value Problem

Abstract

In this paper, we develop a predictor-corrector scheme based on a semi-open and closed-cotes quadrature process for solving an initial value problem of ordinary differential equation. The analysis showed that the method is stable, of order O(h5), and accurate. Numerical examples are given to demonstrate the validity and applicability of the proposed scheme. In addition, the numerical results show that the proposed scheme is very accurate and efficient.