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

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

Open Access

|Feb 2026

Abstract

This study uses the Homotopy analysis method (HAM) and Haar wavelet transform (HWT) to give 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 with linear and nonlinear problems studied. 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

Submitted on: Sep 16, 2024

Accepted on: Jan 12, 2025

Published on: Feb 2, 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.

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