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Abstract
A new algorithm is proposed for the numerical solution of threshold problems in epidemics and population dynamics. These problems are modeled by the delay-differential equations, where the delay function is unknown and has to be determined from the threshold conditions. The new algorithm is based on embedded pair of continuous Runge–Kutta method of order p = 4 and discrete Runge–Kutta method of order q = 3 which is used for the estimation of local discretization errors, combined with the bisection method for the resolution of the threshold condition. Error bounds are derived for the algorithm based on continuous one-step methods for the delay-differential equations and arbitrary iteration process for the threshold conditions. Numerical examples are presented which illustrate the effectiveness of this algorithm.
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Authors (3)
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Zdzisław Jackiewicz
- Arizona State University, Tempe, AZ 85287-1804, United States, AGH University of Science and Technology School of Mathematical and Statistical Sciences, Department of Applied Mathematics
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Y. Kuang
- Arizona State University School of Mathematical and Statistical Sciences
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Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
no. 279,
pages 40 - 56,
ISSN: 0377-0427 - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Bartoszewski Z., Jackiewicz Z., Kuang Y.: Numerical solution of threshold problems in epidemics and population dynamics// JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. -Vol. 279, (2015), s.40-56
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.cam.2014.10.020
- Verified by:
- Gdańsk University of Technology
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