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Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind |
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| Authors: | Hermann Brunner Syvert P. Nørsett |
| Affiliation: | (1) Department of Mathematics, Dalhousie University, B3H 4H8 Halifax, Nova Scotia, Canada;(2) Institutt for Numerisk Matematikk, Norges Tekniske Høgskole, 7034 Trondheim-NTH, Norway;(3) Present address: Institut de Mathématiques, Université de Fribourg, 1700 Fribourg, (Switzerland) |
| Abstract: | Summary This paper deals with the question of the attainable order of convergence in the numerical solution of Volterra and Abel integral equations by collocation methods in certain piecewise polynomial spaces and which are based on suitable interpolatory quadrature for the resulting moment integrals. The use of a (nonlinear) variation of constants formula for the representation of the error function in terms of the defect allows for a unified treatment of equations with continuous and weakly singular kernels. |
| Keywords: | AMS(MOS): 65R20 CR: 5.18 |
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