Development of an Efficient Optimized Hybrid One Step Methods for Solving Fourth-Order Initial Value Problems (IVPs)

This paper examines the development of a one-step optimized block schemes for solving-fourth order initial value problems (IVP) of ordinary differential equations. Interpolation and collocation techniques are considered using approximated power series as the basis function and its fourth derivative as the collocating equation. Two hybrid points and are chosen to achieve optimized errors. The method's properties are analyzed and it is zero stable, consistent and convergent. The application of the method to some fourth-order initial value problems shows the derived method performed better in terms of accuracy and effectiveness; outperforming some existing methods when compared.