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

Narayana, Sachin K.; Devi Kannadasan, Suguntha; Srinivasa, Kumbinarasaiah

doi:10.2478/ijmce-2026-0004

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

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