Numerical Analysis of Differential Equations Using Haar Wavelets

Sheela M.S., Adarsh K.S., D. P. Basti and Channaveerapala Sateesha
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Sheela M.S.: Jain College of Engineering and Technology Department of Mathematics Hubballi, Karnataka, India
Adarsh K.S.: Jain College of Engineering and Technology Department of Physics Hubballi, Karnataka, India
D. P. Basti: S.D.M. College of Engineering and Technology, Department of Mathematics, Dharwad, Karnataka, India 580002
Channaveerapala Sateesha: Government First-Grade College, Department of Mathematics, Koppal, Karnataka, India 583231

International Journal of Research and Innovation in Applied Science, 2025, vol. 10, issue 4, 282-286

Abstract: Wavelet analysis is a rapidly developing field of mathematical and application-oriented research across many scientific disciplines, receiving increasing attention in engineering initiatives. The wavelet transform is localized in both space (time) and frequency, allowing it to extract information from signals that are often impossible to analyze using Fourier or even windowed Fourier transforms. Wavelets serve as effective tools, providing robust mathematical models for scientific phenomena typically represented through linear or nonlinear differential equations. In the present paper, we discuss the Haar wavelet operations and examine the variation of the translation parameter (k) and the dilatation parameter (j); we also consider the second-order differential equations of motion to assess the efficiency and applicability of the intended method. Interestingly, the analysis indicates that the error decreases exponentially as the resolution level increases, leading to more accurate results.

Date: 2025
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