Vieta-Lucas Wavelet based schemes for the numerical solution of the singular models

TL;DR

This paper introduces Vieta-Lucas wavelet-based numerical schemes for solving singular differential equations, providing operational matrices, convergence analysis, and comparative accuracy assessments.

Contribution

It develops new Vieta-Lucas wavelet methods for singular models, including operational matrices and convergence proofs, enhancing numerical solution techniques.

Findings

Methods achieve high accuracy in numerical experiments.

Comparative analysis shows advantages over existing methods.

Error estimates confirm convergence and reliability.

Abstract

In this paper, numerical methods based on Vieta-Lucas wavelets are proposed for solving a class of singular differential equations. The operational matrix of the derivative for Vieta-Lucas wavelets is derived. It is employed to reduce the differential equations into the system of algebraic equations by applying the ideas of the collocation scheme, Tau scheme, and Galerkin scheme respectively. Furthermore, the convergence analysis and error estimates for Vieta-Lucas wavelets are performed. In the numerical section, the comparative analysis is presented among the different versions of the proposed Vieta-Lucas wavelet methods, and the accuracy of the approaches is evaluated by computing the errors and comparing them to the existing findings.