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Stability of finite difference schemes for generalized von Foerster equations with renewal

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to l1 and l∞ norms.
Słowa kluczowe
Rocznik
Strony
375--386
Opis fizyczny
Bibliogr. 15 poz., tab.
Twórcy
  • Institute of Mathematics Wit Stwosz Street 57, 80-952 Gdansk
  • Institute of Mathematics Wit Stwosz Street 57, 80-952 Gdansk
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] F. Brauer, C. Castillo-Chávez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.
  • [3] A.L. Dawidowicz, Existence and uniqueness of solution of generalized von Foerster integro-differential equation with multidimensional space of characteristics of maturity, Bull. Acad. Polon. Sci. Math. 38 (1990), 1–12.
  • [4] A.L. Dawidowicz, K. Łoskot, Existence and uniqueness of solution of some integro--differential equation, Ann. Polon. Math. 47 (1986), 79–87.
  • [5] H. von Foerster, Some remarks on changing populations, [in:] The Kinetics of Cellular Proliferation, Grune and Stratton, New York, 1959.
  • [6] M.E. Gurtin, R. McCamy, Non-linear age-dependent Population dynamics, Arch. Rat. Mech. Anal. 54 (1974), 281–300.
  • [7] A. Lasota, M.C. Mackey, M. Wazewska-Czyzewska, Minimizing therapeutically induced anemia, J. Math. Biol. 13 (1981), 149–158.
  • [8] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Academic Publishers, 1999.
  • [9] P.H. Leslie, The use of matrices in certain population mathematics, Biometrika 33 (1945), 183–212.
  • [10] H. Leszczynski, P. Zwierkowski, Existence of solutions to generalized von Foerster equations with functional dependence, Ann. Polon. Math. 83 (2004) 3, 201–210.
  • [11] H. Leszczynski, P. Zwierkowski, Stability of finite difference schemes for certain problems in biology, Appl. Math. 31 (2004), 13–30.
  • [12] H. Leszczynski, P. Zwierkowski, Iterative methods for generalized von Foerster equations with functional dependence, J. Inequal. Appl. vol. 2007, Article ID 12324, 14 pp., 2007.
  • [13] H. Leszczynski, Differential functional von Foerster equations with reneval, Condensed Matter Physics 54 (2008) 11, 361–370.
  • [14] J.D. Murray, Mathematical biology. 1, An introduction, New York, Springer 2002.
  • [15] J.A. Powell, I. Slapnicar, W. van der Werf, Epidemic spread of a lesion-forming plant pathogen-analysis of a mechanistic model with infinite age structure, Linear Algebra Appl. 398 (2005), 117–140.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3fa11141-113c-4a25-b993-079c57ac1862
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