Application of single step with three generalized hybrid points block method for solving third order ordinary differential equations

Abstract

This article considers the implementation of one step hybrid block method, three generalized hybrid points developed in collocation interpolation approach. The basic numerical properties of the hybrid block method was established and found to be convergent. The efficiency of the new method was confirmed on some initial value problems and found to give better approximation than the existing methods in term of error.

A block hybrid integrator for numerically solving fourth-order Initial Value Problems

“…In this work, we consider linear multistep hybrid formulas with four mid intra-step grid points and fifth derivatives at the two endpoints. These formulas are constructed using a collocation approach, and put together to form a Block Hybrid Method (see [1,5,6,8,9] ).…”

The Simulation of One-Step Algorithms for Treating Higher Order Initial Value Problems

“…The direct approaches for the solution of (1) have been established in literature to be superior to the approach of reducing in terms of approximation, the period of execution and implementation cost [12][13][14]. The linear multistep approaches are most commonly used to solve IVPs as a single formula, and they promote the numerical integration of ordinary differential equation but not self-starting.…”

“…Combining and solving (11), (13) and (15) simultaneously, to give the explicit schemes as y h y h y y…”