Numerical solutions of Volterra integral equation with weakly singular kernel using SCW method

Numerical methods for weakly singular Volterra integral equations are rarely considered in the literature. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the initial point of the interval of integration and bring some difficulties in numerical computation. In this paper, we present a numerical solution of weakly singular Volterra integral equations including the Abels equations by the second Chebyshev wavelet (SCW). We give the SCW operational matrix of fractional integration, and combine with the block pulse functions (BPFs) to derive the procedure of solving this kind integral equations. The proposed method is illustrated with numerical examples. The results reveal that the method is accurate and easy to implement.