A collocation method for the Gurtin-MacCamy equation with finite life-span

SIAM Journal on Numerical Analysis

Volumn 39, Issue 6, 2002, Pages 1914-1937

  Kim, Mi Young ^a   Kwon, Yonghoon ^b  

^a Inha University   (South Korea)

^b Pohang University of Science and Technology (POSTECH)   (South Korea)

Author keywords

Age dependent population dynamics; Collocation method; Implicit Runge Kutta method; Integro differential equation

Indexed keywords

EID: 0036556454     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900370927     Document Type: Article

References (20)

1. L. M. ABIA AND J. C. LÓPEZ-MARCOS, Runge-Kutta methods for age-structured population models, Appl. Numer. Math., 17 (1995), pp. 1-17.
2. T. ARBOGAST AND F. A. MILNER, A finite difference for a two sex model of population dynamics, SIAM J. Numer. Anal., 26 (1989), pp. 1474-1486.
3. C. CHIU, A numerical method for nonlinear age dependent population models, Differential Integral Equations, 3 (1990), pp. 767-782.
4. J. DOUGLAS AND F. MILNER, Numerical methods for a models of population dynamics, Calcolo, 24 (1987), pp. 247-254.
5. G. FAIRWEATHER AND J. C. LOPEZ-MARCOS, A box method for a nonlinear equation of population dynamics, IMA J. Numer. Anal., 11 (1991), pp. 525-538.
6. M. GURTIN AND R. C. MACCAMY, Non-linear age-dependent population dynamics, Arch. Ration. Mech. Anal., 54 (1974), pp. 281-300.
7. M. IANNELLI, Mathematical Theory of Age-Structured Population Dynamics, Applied Mathematics Monographs 7, Comitato Nazionale per le Scienze Matematiche, Consiglio Nazionale delle Ricerche, Giardini-Pisa, Italy, 1995.
8. M. IANNELLI, M.-Y. KIM, AND E.-J. PARK, Asymptotic behavior for an SIS epidemic model and its approximation, Nonlinear Anal., 35 (1999), pp. 797-814.
9. M. IANNELLI, M.-Y. KIM, AND E.-J. PARK, Splitting methods for the numerical approximation of some models of age-structured population dynamics and epidemiology, Appl. Math. Comput., 87 (1997), pp. 69-93.
10. M. IANNELLI, AND F. MILNER, On the Approximation of the Lotka-Mckendrick Equation with Finite Life-Span, Technical report 312, Department of Mathematics, Purdue University, West Lafayette, IN, 1998.
11. M. IANNELLI, F. MILNER, AND A. PUGLIESE, Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission, SIAM J. Math. Anal., 23 (1992), pp. 662-688.
12. A. ISERLES, A first Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Cambridge, UK, 1996.
13. M.-Y. KIM, Qualitative behavior of numerical solutions to an SIS epidemic model, Numer. Methods Partial Differential Equations, 14 (1998), pp. 317-337.
14. M.-Y. KIM, Uniqueness and stability of positive periodic numerical solutions of an epidemic model, in Proceedings of the Fourth Workshop on Differential Equations, Global Analysis Research Center, Kwangju, Korea, 1999, pp. 91-98.
15. M.-Y. KIM AND E.-J. PARK, An upwind scheme for a nonlinear model in age-structured population dynamics, Comput. Math. Appl., 30 (1995), pp. 5-17.
16. M.-Y. KIM AND E.-J. PARK, Long-Time Behavior of Numerical Solutions to Gurtin-MacCamy Equations by Method of Characteristics, preprint.
17. Y. KWON AND C.-K. CHO, Second-order accurate difference methods for a one-sex model of populations dynamics, SIAM J. Numer. Anal., 30 (1993), pp. 1385-1399.
18. F. A. MILNER AND G. RABBIOLO, Rapidly converging numerical algorithms for models of population dynamics, J. Math. Biol., 30 (1992), 733-753.
19. R. A. STRUBLE, Nonlinear Differential Equations, McGraw-Hill New York, 1962.
20. G. F. WEBB, Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, New York, 1985.