Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay |
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Authors: | Bellen Alfredo |
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Affiliation: | 1 Dipartimento di Scienze Matematiche, Universitá di Trieste, 34100 Trieste, Italy |
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Abstract: | In this note we propose a method for the integration of y'(t) = f(t, y(t), y(rt)), 0 t tf y(0) = y0, where 0 < r < 1, by a superconvengent s-stage continuousRK method of discrete global order p and continuous uniformorder q < p 1 for the approximation of the delayedterm y(rt). We prove that, although the maximum attainable orderof the method on an arbitrary mesh is q' = min{p, q + 1}, byusing a quasi-geometric mesh, introduced by Bellen et al. (1997,Appl. Numer. Math. 24, 1997, 279293), the optimal accuracyorder p is preserved. |
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Keywords: | delay differential equations pantograph equation super convergence proportional delay |
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