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Spline collocation methods for nonlinear Volterra integral equations with unknown delay |
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| Authors: | Hermann Brunner Yuri Yatsenko |
| Affiliation: | 1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John''s, Newfoundland, Canada A1C 5S7;2. Glushkov''s Institute of Cybernetics, National Academy of Sciences, 40 Glushkov Ave., Kiev 252207, Ukraine |
| Abstract: | In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation. |
| Keywords: | Nonlinear Volterra integral equations Polynomial spline collocation Local superconvergence Variable memory of dynamical systems Economic-mathematical models |
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