Galerkin method for the Numerical solution of singular boundary value problems using Bernoulli wavelets

Document Type : Regular research papers

Author

Department of Mathematics, Sri Siddeshwar Government First Grade College & P.G. Studies Centre, Nargund-582207, India

Abstract

Singular two-point boundary value problems for ordinary differential equations are commonly encountered in various fields of science and engineering. The numerical solution of these singular boundary value problems (SBVPs) is often challenging due to the presence of singularities in the equations. Wavelets are wave-like oscillations with amplitude that begins at zero and it two basic properties: scale and location. Scale defines how “stretched” or “squished” a wavelet is. This property is related to frequency as defined for waves. Location defines where the wavelet is positioned in time. Wavelets enable the decomposition of complex information, such as music, speech, images, and patterns, into simpler components at various positions and scales, which can then be accurately reconstructed. This paper presents a Galerkin method for solving SBVPs numerically using Bernoulli wavelets. It includes numerical examples that illustrate the method's accuracy, applicability, and usefulness. The findings indicate that the method is highly effective, straightforward, and easy to implement.

Keywords

Main Subjects

Files

History

  • Receive Date: 27 January 2025
  • Revise Date: 01 June 2025
  • Accept Date: 30 June 2025

Share

How to cite

Statistics