Theoretical Mathematics & Applications

3-Step y- function hybrid methods for direct numerical integration of second order IVPs in ODEs

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• Abstract

  This article is concerned with implicit y-function hybrid numerical methods for direct integration solution of general second-order differential equations. The approach is based on interpolation of the basis function at both grid and off-grid points and collocation of its associated differential system at all grid points using power series as the basis function to the solution of the problem. The methods developed are continuous, consistent, and symmetric and the main predictor of the same order of accuracy with the methods was also developed to evaluate the implicit scheme. Comparisons of results of the derived methods with existing methods of higher order of accuracy show that the proposed method is better than the existing methods.