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

Authors

  • Folashade Mistura Jimoh
    Department of Physical Sciences, Al-Hikmah University, Ilorin, Nigeria
  • Adam Ajimoti Ishaq
    Department of Physical Sciences, Al-Hikmah University, Ilorin, Nigeria
  • Kazeem Issa
    Department of Mathematics and Statistics, Kwara State University, Ilorin, Nigeria

Keywords:

Ordinary differential equations, Higher-order oscillatory problems, Linear block method, Computational efficiency

Abstract

In many areas of science and engineering, problems modeled by ordinary differential equations (ODEs) often lack analytical solutions, requiring the use of numerical methods for approximation. The proposed method tackles the challenges of solving higher-order oscillatory differential equations and introduces a new linear block technique for directly solving these equations. This method improves accuracy, reduces computational effort, and simplifies coding complexity compared to previous approaches. A generalized algorithm is presented to derive the proposed method, which enhances existing techniques for second-order and higher-order oscillatory problems. The basic properties of the method were numerically analyzed, confirming its accuracy, stability, consistency, and convergence. The proposed method proves to be efficient and suitable for various test problems, including real-life problems, which demonstrate its accuracy as compared to the existing methods.
Dimensions

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An A-stable region of absolutely stability.

Published

2025-07-02

How to Cite

Approximate solution of higher-order oscillatory differential equations via modified linear block techniques. (2025). African Scientific Reports, 4(2), 275. https://doi.org/10.46481/asr.2025.4.2.275

Issue

Volume 4, Issue 2, August 2025

Section

MATHEMATICAL SCIENCES SECTION
Copyright & Licensing

Copyright (c) 2025 Folashade Mistura Jimoh, Adam Ajimoti Ishaq, Kazeem Issa

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Approximate solution of higher-order oscillatory differential equations via modified linear block techniques. (2025). African Scientific Reports, 4(2), 275. https://doi.org/10.46481/asr.2025.4.2.275

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