3-Step Block Hybrid Linear Multistep Methods for solution of Special Second Order Ordinary Differential Equations

Abstract

This paper presents set of two (2) Implicit Hybrid Block Methods which are derived through multistep collocation method using power series as a basic function for generating solution of special second order ordinary differential equations. The derived continuous forms which are evaluated at some grids and off-grid points of collocation and interpolation to form the block hybrid methods for step number k=3. The discrete schemes obtained possess uniformly high order and found to be zero-stable, consistent and hence convergent. Some numerical examples are given to test the accuracy and efficiency advantages. The results of our evaluation show that our methods outperform reviewed work.