A Block Hybrid Scheme for the Solution of First Order Ordinary Differential Equations

Abstract

A new hybrid linear multistep method (LMM) is considered for the solution of first order initial value problems (IVPs). The new hybrid method is an extension of LMM by the inclusion of extra intermediate off-step points in between the usual grid points in the numerical schemes. A detailed analysis of the method such as the local truncation error and order, consistency and zero stability are investigated and presented. The method as compared with other recently derived methods provide approximation of high accuracy to solution of IVPs in ordinary differential equations.