A study on different classes of differential equations by semi-analytical and numerical techniques

Sachin K. Narayana; Suguntha Devi Kannadasan; Kumbinarasaiah Srinivasa

doi:10.2478/ijmce-2026-0004

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A study on different classes of differential equations by semi-analytical and numerical techniques

International Journal of Mathematics and Computer in Engineering

Volume 4 (2026): Issue 1 (June 2026)

By: Sachin K. Narayana, Suguntha Devi Kannadasan and Kumbinarasaiah Srinivasa

Open Access

|May 2026

Abstract

This study applies the Homotopy analysis method (HAM) and Haar wavelet transform (HWT) in order to provide an innovative technique for approximating to the nonlinear ordinary differential equations (ODEs), a system of ODEs, and partial differential equations (PDEs). HAM is a potent semi-analytical method that works well when studying linear and nonlinear problems. HWT is a numerical technique that effectively discretizes differential equations (DEs) simultaneously. A robust analytical method builds a family of equations that smoothly transforms the original nonlinear equation into a straightforward linear issue using the topological concept of homotopy. This allows the derivation of extremely precise series solutions. Real-world application problems are solved to analyze the correctness and effectiveness of the projected system.

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Articles in this issue

DOI: https://doi.org/10.2478/ijmce-2026-0004 | Journal eISSN: 2956-7068

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Language: English

Page range: 45 - 64

Submitted on: Sep 16, 2024

Accepted on: Jan 12, 2025

Published on: May 27, 2026

Published by: Harran University

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Ordinary differential equations,

HAM,

Haar wavelet,

PDES,

HWT

Related subjects:

Computer sciences,

Computer sciences, other,

Engineering,

Introductions and overviews,

Physics,

© 2026 Sachin K. Narayana, Suguntha Devi Kannadasan, Kumbinarasaiah Srinivasa, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 4 (2026): Issue 1 (June 2026)