A discrete collocation method for Fredholm integro-differential equations with weakly singular kernels |
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Authors: | Arvet Pedas Enn Tamme |
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Institution: | Institute of Mathematics, University of Tartu, Liivi 2, 50409 Tartu, Estonia |
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Abstract: | A fully discrete version of a piecewise polynomial collocation method is constructed to solve initial or boundary value problems of linear Fredholm integro-differential equations with weakly singular kernels. Using an integral equation reformulation and special graded grids, optimal global convergence estimates are derived. For special values of parameters an improvement of the convergence rate of elaborated numerical schemes is established. Some of our theoretical results are illustrated by numerical experiments. |
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Keywords: | Weakly singular integro-differential equation Discrete collocation method Product integration Graded grid |
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