Abstract
Spectral collocation methods are developed for weakly singular Volterra integro-differential equations (VIDEs). Convergence analysis results show that global convergence order depends on the regularities of the kernels functions and solutions to VIDEs, and the number of collocation points is independent of regularities of given functions and the solution to VIDEs. Numerical experiments are carried out to confirm these theoretical results. In numerical experiments, we develop a numerical scheme for nonlinear VIDEs, and investigate the local convergence on collocation points.
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