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

摘要

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 L2 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.