Three-Step Hybrid Linear Multistep Method for Solution of First Order Initial Value Problems in Ordinary Differential Equations

Abstract

In this article, a three-step hybrid linear multistep method for solution of first order initial value problems (IVPs) in ordinary differential differential equations (ODEs) is proposed. Essentially, the method is based on collocation of the differential system and the interpolation of the approximate solution at the grid and off-grid points. Evaluation of the proposed method at Χ=Χ_n+k and Χ_n+5/2 yields a class of two discrete schemes of order 7 which are not self-starting. Furthermore, a selfstarting method is adopted. The proposed method is consistent, zero stable and convergent. Finally, the accuracy of the method is tested on some standard IVPs.

Keywords: , linear multistep, initial value problems, collocation,   interpolation, consistent, zero stable and convergent