Advances in Moduli of Continuity Through Generalized Chebyshev Wavelet Approximation: Applications to Mathematical Models

Abstract

In this work, we introduce the generalized Chebyshev wavelet over [0,l). We estimate the generalized Chebyshev wavelet approximation of solution functions belonging to the generalized H\"older's class, along with their modulus of continuity. The modulus of continuity is a mathematical tool for measuring a function's smoothness and describing its properties on local and global levels. We aim to integrate moduli of continuity into wavelet approaches that significantly enhances the precision and effectiveness of solutions in diverse mathematical and engineering domains. Additionally, we propose a numerical algorithm based on collocation techniques using the generalized Chebyshev wavelet. We compare our outcomes with the results obtained by other methods that are documented in the literature. The analysis shows that the proposed method is remarkably efficient and precise depicted by the facts and figures of this research.