A note on Jacobi spectral-collocation methods for weakly singular Volterra integral equations with smooth solutions

Abstract

This work is concerned with spectral Jacobi-collocation methods for Volterra integral equations of the second kind with a weakly singular of the form (t-s)-α. When the underlying solutions are sufficiently smooth, the convergence analysis was carried out in [Chen & Tang, J. Comput. Appl. Math., 233 (2009), pp. 938-950]; due to technical reasons the results are restricted to 0 < μ < 1/2 In this work, we will improve the results to the general case 0 < μ < 1 and demonstrate that the numerical errors decay exponentially in the infinity and weighted norms when the smooth solution is involved. Copyright 2013 by AMSS, Chinese Academy of Sciences.