On the order of the error in discretization methods for weakly singular second kind non-smooth solutions |
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Authors: | Jennifer Dixon |
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Institution: | (1) Oxford University Computing Laboratory, 8–11 Keble Road, OX1 3QD Oxford, England |
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Abstract: | In general, second kind Volterra integral equations with weakly singular kernels of the formk(t,s)(t –s)–
posses solutions which have discontinuous derivatives att=0. A discrete Gronwall inequality is employed to prove that, away from the origin, the error in product integration and collocation schemes for these equations is of order 2-. |
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Keywords: | Volterra equations weakly singular kernels non-smooth solutions product integration error analysis |
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