AN EFFICIENT MODIFIED OPTIMAL HYBRID BLOCK METHOD FOR SOLUTION FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this article, modified optimal hybrid block method is proposed for the solution of first-
order ordinary differential equations. The techniques of interpolation and collocation were
adopted for the derivation of the methods using a three-parameter approximation. The hybrid
points were obtained by minimizing the local truncation error of the main method. The
schemes obtained were reformulated to reduce the number of function evaluation. The
discrete schemes were produced as a by-product of the continuous scheme and used to
simultaneously solve initial value problems (IVPs) in block mode. The resulting schemes are
self-starting, do not require the creation of individual predictors, consistent, zero-stable, and
convergent. The accuracy and efficiency of the methods were ascertained using several
numerical experiments. The numerical results were favorably compared to some techniques
from the cited literature.