×

zbMATH — the first resource for mathematics

The tracking of derivative discontinuities in systems of delay- differential equations. (English) Zbl 0747.65054
A model for tracking of derivative discontinuities in systems of evolutionary delay-differential equations is presented.

MSC:
65L05 Numerical methods for initial value problems
34K05 General theory of functional-differential equations
Software:
DELSOL
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bader, G., Ein mehrschrittverfahren mit variabler schrittweite und variabler ordnung zur integration von systemen retardierter differentialgleichungen mit zustan dabhängigier verzögerung, (1983), Diplomarbeit von Volker Haller Universität Heidelberg
[2] Bellen, A., One-step collocation for delay-differential equations, J. comput. appl. math., 10, 275-285, (1984) · Zbl 0538.65047
[3] Bellen, A.; Zennaro, M., Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method, Numer. math., 47, 301-316, (1985) · Zbl 0577.65064
[4] Bock, H.G.; Schlöder, J., The numerical solution of retarded differential equations with state dependent time lags, Z. angew. math. mech., 61, 269-271, (1981)
[5] El’sgol’ts, L.E.; Norkin, S.B., Introduction to the theory and applications of differential equations with deviating arguments, (1973), Academic Press New York · Zbl 0287.34073
[6] Neves, K.W.; Feldstein, A., Characterization of jump discontinuities for state dependent differential equations, J. math. anal. appl., 56, 689-707, (1977) · Zbl 0348.34054
[7] Feldstein, A.; Neves, K.W., High order methods for state dependent delay differential equations with non-smooth solutions, SIAM J. numer. anal., 21, 844-864, (1984) · Zbl 0572.65062
[8] Hairer, E.; Nørsett, S.P.; Wanner, G., Solving ordinary differential equations I, () · Zbl 1185.65115
[9] Hügel, R., Numerischer vergleich von programmen zur Lösung von delay gleichungen, (1985), Westfälische Wilhelms-Universität Münster, West Germany, 5/85 N
[10] Neves, K.W., Automatic integration of functional differential equations. an approach, ACM trans. math. software, 1, 357-368, (1975) · Zbl 0315.65045
[11] Oppelstrup, J., Delay 1 - a program for integrating delay-differential equations, ()
[12] Paul, C., Concerning explicit Runge-Kutta techniques for delay differential equations, ()
[13] Shampine, L.F.; Gordon, M.K., Computer solution of ordinary differential equations, (1975), Freeman New York · Zbl 0347.65001
[14] Willé, D.R., The numerical solution of delay-differential equations, () · Zbl 0832.65064
[15] Willé, D.R.; Baker, C.T.H., The propagation of derivative discontinuities in systems of delay-differential equations, () · Zbl 0832.65064
[16] Willé, D.R.; Baker, C.T.H., The tracking of derivative discontinuities in systems of delay-differential equations, () · Zbl 0832.65064
[17] Willé, D.R.; Baker, C.T.H., DELSOL — a numerical code for the solution of systems of delay-differential equations, Appl. numer. math., 9, 223-234, (1992), (this issue). · Zbl 0747.65055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.