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。推导了Vieta-Lucas小波的导数运算矩阵。通过分别应用配点法、Tau方法和Galerkin方法的思想，该运算矩阵被用于将微分方程转化为代数方程组。此外，还对Vieta-Lucas小波进行了收敛性分析和误差估计。在数值部分，对所提出的Vieta-Lucas小波方法的不同版本进行了对比分析，并通过计算误差并将其与现有结果进行比较，评估了这些方法的精度。