Two-step two-point hybrid methods for general second order differential equations

摘要

Two-step two-point hybrid numerical methods for direct solution of initial value problems of general second order differential equations are proposed in this study. Chebyshev polynomials without perturbation terms are used as basic function for the development of the methods in predictor-corrector mode. The collocation and interpolation equations are generated at both grid and off-grid points. The resulting methods are zero-stable, consistent and normalized. The main predictors, having the same order with the scheme, are developed for the implementation of the methods. Accuracy of a discrete scheme from the methods is tested with linear and non-linear problems. The results show a better performance over the existing methods.