Abstract
Weakly singular Volterra integral equations of the different types are considered. The construction of accuracy-optimal numerical methods for one-dimensional and multidimensional equations is discussed. Since this question is closely related with the optimal approximation problem, the orders of the Babenko and Kolmogorov $n$-widths of compact sets from some classes of functions have been evaluated. In conclusion we adduce some numerical illustrations for 2-D Volterra equations.
Citation
I.V. Boykov. A.N. Tynda. "Numerical methods of optimal accuracy for weakly singular Volterra integral equations." Ann. Funct. Anal. 6 (4) 114 - 133, 2015. https://doi.org/10.15352/afa/06-4-114
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