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We analyse a finite difference scheme for von Foerster-McKendrick type equations with functional dependence forward in time and backward with respect to one dimensional spatial variable. Some properties of solutions of a scheme are given. Convergence of a finite difference scheme is proved. The presented theory is illustrated by a numerical example.
Wydawca
Czasopismo
Rocznik
Tom
Strony
725--737
Opis fizyczny
Bibliogr. 9 poz.
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autor
- Institute Of Mathematics University Of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland, zwierkow@mat.ug.edu.pl
Bibliografia
- [1] A. S. Ackleh, K. Deng, X. Wang, Competitive exclusion and coexistence for a quasilinear size-structured population model, Math. Biosci. 192 (2004), 177–192.
- [2] A. L. Dawidowicz, K. Łoskot, Existence and uniqueness of solution of some integrodifferential equation, Ann. Polon. Math. 47 (1986), 79–87.
- [3] M. E. Gurtin, R. McCamy, Non-linear age-dependend population dynamics, Arch. Ration. Mech. Anal. 54 (1974), 281–300.
- [4] J. K. Hale, S. V. Lunel, Introduction to Functional Differential Equations, Springer, New York, Applied Mathematical Sciences Vol. 99, 1993.
- [5] D. Jaruszewska-Walczak, Z. Kamont, Difference methods for quasilinear hyperbolic differential functional systems on the Haar pyramid, Bull. Belg. Math. Soc. 10 (2003), 267–290.
- [6] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Academic Publishers, 1999.
- [7] A. Lasota, M. C. Mackey, M. Ważewska-Czyżewska, Minimizing therapeutically induced anemia, J. Math. Biol. 13 (1981), 149–158.
- [8] H. Leszczyński, P. Zwierkowski, Stability of finite difference schemes for certain problems in biology, Appl. Math. 31 (2004), 13–30.
- [9] H. Leszczyński, P. Zwierkowski, Iterative methods for generalized von Foerster equations with functional dependence, J. Inequal. Appl., vol. 2007, Article ID 12324, 14 pages, 2007. doi:10.1155/2007/12324
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Bibliografia
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bwmeta1.element.baztech-article-PWA4-0035-0019