An explicit third-order numerical method for size-structured population equations

Numerical Methods for Partial Differential Equations

Volumn 19, Issue 1, 2003, Pages 1-21

  Kostova, Tanya ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Difference schemes; Error analysis; Quadratures; Structured population dynamics

Indexed keywords

EID: 0037232159     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.10037     Document Type: Article

References (21)

1. 1 M. Iannelli, Mathematical theory of age—structured population dynamics, Applied Mathematical Monographs, C.N.R.I., 1995.
2. 2 G. F. Webb, Theory of age‐dependent population dynamics, Marcel Dekker, New York, 1985.
3. 3 A. M. de Roos, Numerical methods for structured population models: The escallator boxcar train, Numer Methods Partial Differential Eq 4 (1988), 173–195.
4. 4 T. H. Barr, Approximation for age‐structured population models using projection methods, Comput Math Appl 21 (5) (1991), 17–40.
5. 5 F. Kappel and K. Zhang, Approximation of linear age‐structured population models using Legendre polynomials, J Math Anal Appls 180 (1993), 518–549.
6. 6 T. Arbogast and F. A. Milner, A finite difference for a two‐sex model of population dynamics, SIAM J Numer Anal 26 (1989), 1474–1486.
7. 7 J. Douglas, Jr., and F. A. Milner, Numerical methods for a model of population dynamics, Calcolo 24 (1987), 247–254.
8. 8 T. V. Kostova, Numerical solutions of a hyperbolic differential‐integral equation, Comput Math Appl 15 (1988), 427–436.
9. 9 T. V. Kostova and M. Marcheva, Numerical solutions to the Gurtin‐MacCamy equation, Math Balkanica 3 (1988), 264–277.
10. 10 T. V. Kostova, Numerical solutions to equations modelling nonlinearly interacting age‐dependent populations, Comput Math Appl 18 (1990), 95–103.
11. 11 J. C. Lopez‐Marcos, An upwind scheme for a nonlinear hyperbolic integro‐differential equation with integral boundary condition, Comput Math Appl 22 (1991), 15–28.
12. 12 G. Fairweather and J. C. Lopez‐Marcos, A box method for a nonlinear equation of population dynamics, IMA J Numer Anal 11 (1991), 525–538.
13. 13 G. Fairweather and J. C. Lopez‐Marcos, An explicit extrapolated box scheme for the Gurtin‐MacCamy equation, Comput Math Appl 27 (1994), 41–53.
14. 14 L. M. Abia and J. C. Lopez‐Marcos, On the numerical integration of non‐local terms for age‐structured population models, Math Biosci 157 (1999), 147–168.
15. 15 Y. Kwon and C.‐K. Cho, Second order accurate difference methods for a one‐sex model of population dynamics, SIAM J Numer Anal 30 (1993), 1385–1399.
16. 16 F. A. Milner and G. Rabbiolo, Rapidly converging numerical algorithms for models of population dynamics, J Math Biol 30 (1992), 733–753.
17. 17 L. M. Abia and J. C. Lopez‐Marcos, Runge‐Kutta methods for age‐structured population models, Appl Numer Math 17 (1995), 1–17.
18. 18 K. Ito, F. Kappel, and G. Peichl, A fully discretized approximation scheme for size‐structured population models, SIAM J Numer Anal 28 (1991), 923–954.
19. 19 O. Angulo and J. C. Lopez‐Marcos, Numerical schemes for size‐structured population models, Math Biosci 157 (1999), 169–188.
20. 20 O. Angulo and J. C. Lopez‐Marcos, Numerical integration of nonlinear size‐structured population equations, Ecol Model 133 (2000), 3–14.
21. 21 H. Brunner and P. J. van der Houwen, The numerical solution of Volterra equations, CWI Monograph 3, North Holland, Amsterdam, 1986.