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.

翻译：本文提出了基于Vieta-Lucas小波的数值方法，用于求解一类奇异微分方程。导出了Vieta-Lucas小波的导数运算矩阵。通过分别应用配点法、Tau法和Galerkin法的思想，将该运算矩阵用于将微分方程简化为代数方程组。此外，对Vieta-Lucas小波进行了收敛性分析和误差估计。在数值实验部分，对提出的不同版本Vieta-Lucas小波方法进行了比较分析，并通过计算误差并与现有结果进行对比，评估了这些方法的精度。