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) |