On some computational aspects of Hermite wavelets on a class of SBVPs arising in exothermic reactions

TL;DR

This paper introduces Hermite wavelet collocation methods for solving singular boundary value problems related to exothermic reactions, demonstrating their stability and efficiency through comparison with Haar wavelets and application to Lane-Emden equations.

Contribution

It presents four new stable computational methods using Hermite wavelets for solving nonlinear SBVPs, with convergence analysis and comparison to Haar wavelets.

Findings

Hermite wavelet methods are computationally stable and efficient.

The methods outperform Haar wavelet collocation in accuracy.

Successful application to Lane-Emden equations confirms effectiveness.

Abstract

We propose a new class of SBVPs which deals with exothermic reactions. We also propose four computationally stable methods to solve singular nonlinear BVPs by using Hermite wavelet collocation which are coupled with Newton's quasilinearization and Newton-Raphson method. We compare the results obtained with Hermite Wavelets with Haar wavelet collocation. The efficiency of these methods are verified by applying these four methods on Lane-Emden equations. Convergence analysis is also presented.