The Double Step Hybrid Linear Multistep Method for Solving Second Order Initial Value Problems
Y. Skwame
Department of Mathematics, Adamawa State University, Mubi, Nigeria.
J. Z. Donald
Department of Mathematics, Adamawa State University, Mubi, Nigeria.
T. Y. Kyagya
Department of Mathematics and Statistic, Federal University, Wukari, Nigeria.
J. Sabo *
Department of Mathematics, Adamawa State University, Mubi, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we develop the double step hybrid linear multistep method for solving second order initial value problems via interpolation and collocation method of power series approximate solution to give a system of nonlinear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep method is solved for the independent solutions to give a continuous hybrid block method which is then evaluated at some selected grid points to give a discrete block method.
The basic numerical properties of the hybrid block method was established and found to be zero-stable, consistent and convergent. The efficiency of the new method was conformed on some initial value problems and found to give better approximation than the existing methods.
Keywords: Double step, HLMM, IVPs, interpolation and collocation, power series.