TY - JOUR
T1 - Discrete variable methods for delay-differential equations with threshold-type delays
AU - Jackiewicz, Zdzislaw
AU - Zubik-Kowal, B.
N1 - Funding Information:
The authors wish to express their gratitude to anonymous referees for their helpful comments. The first author was partially supported by NSF grant DMS–0509597.
PY - 2009/6/15
Y1 - 2009/6/15
N2 - We study numerical solution of systems of delay-differential equations in which the delay function, which depends on the unknown solution, is defined implicitly by the threshold condition. We study discrete variable numerical methods for these problems and present error analysis. The global error is composed of the error of solving the differential systems, the error from the threshold conditions and the errors in delay arguments. Our theoretical analysis is confirmed by numerical experiments on threshold problems from the theory of epidemics and from population dynamics.
AB - We study numerical solution of systems of delay-differential equations in which the delay function, which depends on the unknown solution, is defined implicitly by the threshold condition. We study discrete variable numerical methods for these problems and present error analysis. The global error is composed of the error of solving the differential systems, the error from the threshold conditions and the errors in delay arguments. Our theoretical analysis is confirmed by numerical experiments on threshold problems from the theory of epidemics and from population dynamics.
KW - Delay-differential systems
KW - Error analysis
KW - Numerical approximations
KW - Threshold conditions
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U2 - 10.1016/j.cam.2008.03.022
DO - 10.1016/j.cam.2008.03.022
M3 - Article
AN - SCOPUS:64549138036
SN - 0377-0427
VL - 228
SP - 514
EP - 523
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -