Convergence analysis of spectral collocation methods for a class of weakly singular Volterra integral equations

Abstract In this paper, we discuss the application of spectral Jacobi-collocation methods to a certain class of weakly singular Volterra integral equations. First, we use some function transformations and variable changes to transform the equation into a Volterra integral equation defined on the standard interval [ - 1 , 1 ] . Then the Jacobi–Gauss quadrature formula is used to approximate the integral operator. For the spectral Jacobi-collocation method, a rigorous error analysis in both the L ∞ and weighted L 2 norms is given under the assumption that both the kernel function and the source function are sufficiently smooth. Finally, some numerical examples are provided to illustrate the theoretical results.