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EnglishWe introduce Runge–Kutta (RK) methods for Retarded Functional Differential Equations (RFDEs).With respect to RK methods (A, b, c) for Ordinary Differential Equations the weights vector b ∈ Rs and the coefficients matrix A ∈ Rs×s are replaced by Rsvalued and Rs×s-valued polynomial functions b(·) and A(·) respectively. Such methods for RFDEs are different from Continuous RK (CRK) methods where only the weights vector is replaced by a polynomial function. We develop order conditions and construct explicit methods up to the convergence order four.
| Titolo: | Runge-Kutta Methods for Retarded Functional Differential Equations |
| Autori: | |
| Data di pubblicazione: | 2005 |
| Rivista: | |
| Abstract: | We introduce Runge–Kutta (RK) methods for Retarded Functional Differential Equations (RFDEs).With respect to RK methods (A, b, c) for Ordinary Differential Equations the weights vector b ∈ Rs and the coefficients matrix A ∈ Rs×s are replaced by Rsvalued and Rs×s-valued polynomial functions b(·) and A(·) respectively. Such methods for RFDEs are different from Continuous RK (CRK) methods where only the weights vector is replaced by a polynomial function. We develop order conditions and construct explicit methods up to the convergence order four. |
| Handle: | http://hdl.handle.net/11368/1697476 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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