Skip to content
Research Article Open access CC BY 4.0

On the Numerical Approximation of Higher Order Differential Equation

Donald J. Zirra, Yusuf Skwame, Sabo John, Joshua A. Kwanamu, Silas Daniel

Asian Journal of Research and Reviews in Physics · pp. 1–26 · Published 4 Jan 2024

10.9734/ajr2p/2024/v8i1154

Abstract

This research examines the general K - step block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied. Some distinct fourth order oscillatory differential equation were directly applied on the new method in order to overcome the setbacks in reduction method, where the step size varies. The results obtained were compared with those in literature and the new method takes away the burden of solving fourth order oscillatory differential equations. The accuracy of the new method proved to be better as it outperformed those of existing methods. Therefore, from the results, the new method has shown better accuracy and faster convergence graphically. One of the advantage of the new method is that it does not require much computational burden and it is also self-starting.

Accuracy computational burden higher order IVPs linear block approach

References (7)

  1. 1 On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems [DOI]
  2. 2 A New Special 15-Step Block Method for Solving General Fourth Order Ordinary Differential Equations [DOI]
  3. 3 Numerical Solution of Stiff and Oscillatory Problems using Third Derivative Trigonometrically Fitted Block Method [DOI]
  4. 4 Implicit Four-Point Hybrid Block Integrator for the Simulations of Stiff Models [DOI]
  5. 5 Implicit five-step block method with generalised equidistant points for solving fourth order linear and non-linear initial value problems [DOI]
  6. 6 On the Simulation of Higher Order Linear Block Algorithm for Modelling Fourth Order Initial Value Problems [DOI]
  7. 7 A One-Step Block Hybrid Integrator for Solving Fifth Order Korteweg-de Vries Equations [DOI]

Cited by 1

Approximate solution of higher-order oscillatory differential equations via modified linear block techniques

Folashade Mistura Jimoh, Adam Ajimoti Ishaq, Kazeem Issa · African Scientific Reports · 2025

Related research

Article metrics

Real usage data collected on this platform.

41

Page views

0

PDF downloads

4

Outbound clicks

1

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.