Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique - Youssef Esmaiel; Magdi El-Azab; Galal El-Baghdady (Computational Algorithms and Numerical Dimensions)
This study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented. By employing these polynomials, the singular Volterra integral equation is transformed into a set of algebraic equations that need to be solved. Subsequently, numerical analysis is introduced, followed by some examples and a comparison of them with existing methods to demonstrate the soundness and practicality of our method.