Development and Implementation of Four-Step Predictor-Corrector Method with an Improvement Strategy for Fourth-Order Ordinary Differential Equations with Applications

This article focuses on the development, theoretical analysis, and implementation of a four-level predictor-corrector method with an improved strategy for solving fourth-order ordinary differential equations using initial conditions. When developing the method, Chebyshev polynomials of the first kind were adopted as the basis functions for solving the IVP. Chebyshev polynomials of the first kind were interpolated at some selected grid and off-grid points, and the fourth derivative of the approximate solution was collocated at all grid and off-grid points. The methods was derived and implemented in such a way that the correctors are of the same order with the predictors in other to overcome setbacks associated with existing predictor-corrector, thus enhanced a better accuracy and stability. Theoretical analysis of the methods were validated to ensure that the methods are usable and efficient. The methods was applied to three numerical test problems in order to establish the accuracy of the methods. The results show better accuracy over some existing approach in the literature.