Haar wavelet quasilinearization technique for doubly singular boundary value problems

TL;DR

This paper introduces a Haar wavelet-based quasilinearization method for efficiently solving a broad class of doubly singular boundary value problems, demonstrating rapid convergence and high accuracy through numerical experiments.

Contribution

It presents a novel combination of Haar wavelet and quasilinearization techniques specifically for doubly singular boundary value problems, with proven convergence and applicability.

Findings

Achieves second-order convergence of the solution sequence.

Provides accurate numerical solutions for eight different singular problems.

Demonstrates superiority over existing methods in terms of accuracy and convergence.

Abstract

The Haar wavelet based quasilinearization technique for solving a general class of singular boundary value problems is proposed. Quasilinearization technique is used to linearize nonlinear singular problem. Second rate of convergence is obtained of a sequence of linear singular problems. Numerical solution of linear singular prob- lems is obtained by Haar-wavelet method. In each iteration of quasilinearization technique, the numerical solution is updated by the Haar wavelet method. Conver- gence analysis of Haar wavelet method is discussed. The results are compared with the results obtained by the other technique and with exact solution. Eight singular problems are solved to show the applicability of the Haar wavelet quasilinearization technique.