Wavelet Based Galerkin Method for the Numerical Solution of Singular Boundary Value Problems using Fibonacci Wavelets

Abstract

Singular boundary value problems (SBVPs) have become prevalent in scientific applications such as gas dynamics, chemical reactions, and structural mechanics. In review, the numerical approximation of solutions to differential equations serves as a crucial mechanism across various scientific and engineering fields, facilitating the assessment and analysis of complex systems that are not readily solvable through analytical methods.  Due to this, the numerical methods are very crucial. As a result, numerical methods are of significant importance.  So, the wavelet-based Galerkin method using Fibonacci wavelets for the numerical solution of SBVPs is introduced. The paper also provides illustrative examples to demonstrate the effectiveness and accuracy of the method.