Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations |
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Authors: | Tao Tang |
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Affiliation: | (1) Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6 Burnaby, British Columbia, Canada |
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Abstract: | Summary We discuss the application of a class of spline collocation methods to first-order Volterra integro-differential equations (VIDEs) which contain a weakly singular kernel (t–s)– with 0<<1. It will be shown that superconvergence properties may be obtained by using appropriate collocation parameters and graded meshes. The grading exponents of graded meshes used are not greater thanm (the polynomial degree) which is independent of . This is in contrast to the theories of spline collocation methods for Volterra (or Fredholm) integral equation of the second kind. Numerical examples are given to illustrate the theoretical results. |
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Keywords: | 65R20 45D05 |
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