Numerical solution of threshold problems in epidemics and population dynamics

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:279

Article

Bartoszewski, Z.¹  Jackiewicz, Z.^2,3  Kuang, Y.² 

[1] Gdansk Univ Technol, Dept Appl Phys & Math, PL-80233 Gdansk, Poland

[2] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

[3] AGH Univ Sci & Technol, Dept Appl Math, PL-30059 Krakow, Poland

关键词: Delay-differential equations;    Threshold conditions;    Continuous Runge-Kutta methods;    Bisection method;    Local error estimation;    Convergence analysis;   

DOI  :  10.1016/j.cam.2014.10.020

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free