Approximation and Moduli of continuity of functions in H¨older class Hα[0, μ), μ > 0 and wavelet solutions of singular differential equations

Abstract

This paper introduces a precise upper limit for solving the numerical solutions of singular differential equations by employing error analysis. The approach utilizes extended second-kind Chebyshev wavelets to solve the singular differential equation. By applying the exact upper bound based on the moduli of continuity in the H¨older space interval [0, μ), it becomes evident that the method exhibits convergence with a reduced number of wavelet coefficients. Additionally, the paper includes several numerical examples that effectively showcase the method’s validity and applicability