Uniform Order Zero- Stable K-Step Block Methods For Initial Value Problems Of Ordinary Differential Equations

Abstract

Efficient and accurate uniform order hybrid block methods are proposed in this paper. Specifically the schemes are of uniform order 4 for ki (i=2,3). The block schemes are adequate, and accurate and also yield good stability properties. The traditional implementation of single step method is avoided by new proposed method over block steps, which requires no starting value. Moreover the speed of integration is enhanced for k_i (i=2,3) by 2k and (2k-1)   successive steps movement at a time (block steps). Numerical examples are given to illustrate the performance of the new procedures.

Keywords: Zero stability, Hybrid, k –step, Block methods, first order initial value problem