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Optimality of theoretical error estimates for spline collocation methods for linear weakly singular Volterra integro-differential equations. (English) Zbl 1188.65177

Summary: Two spline collocation methods for solving linear weakly singular Volterra integrodifferential equations are considered. A result on the superconvergence at the collocation points is proved and optimality of several theoretical error estimates is demonstrated by extensive numerical experiments. Based on numerical results, a conjecture about the theoretical error estimates at the collocation points is stated for the cases not covered by known theorems.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)