# The Double Step Hybrid Linear Multistep Method for Solving Second Order Initial Value Problems

## 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.

## Article Details

How to Cite
Skwame, Y., Donald, J. Z., Kyagya, T. Y., & Sabo, J. (2019). The Double Step Hybrid Linear Multistep Method for Solving Second Order Initial Value Problems. Asian Research Journal of Mathematics, 15(2), 1-11. https://doi.org/10.9734/arjom/2019/v15i230145
Section
Original Research Article

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