Numerical method for solving an inverse problem for a population model
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 490-500
A. M. Denisov; A. S. Makeev. Numerical method for solving an inverse problem for a population model. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 490-500. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a12/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The inverse problem of determining the growth rate coefficient of biological objects from additional information on their time-dependent density is considered. Two nonlinear integral equations are derived for the unknown coefficient, which is determined on part of its domain from one equation and on the remaining part from the other equation. The nonlinear integral equations are solved by iterative methods. The convergence conditions for the iterative methods are formulated, and results of numerical experiments are presented.

[1] Murray J. D., Biology, Springer, New York, 1993

[2] Banks H. J., Kappel F., “Transformation semigroups and $L^1$-approximation for size structured population models”, Semigroup Forum., 38 (1989), 141–155 | DOI | MR | Zbl

[3] Banks H. T., Kappel F., Wang C., “Weak solutions and differentiability for size structured population models”, Internat. Ser. Numer. Math., 100 (1991), 35–50 | MR | Zbl

[4] Ackleh A. S., Deng K., “Monotone method for first order nonlocal hyperbolic initial-boundary value problems”, Applic. Analys., 67 (1997), 283–293 | DOI | MR | Zbl

[5] Sinko J. W., Streifer W., “A new model for age-sized structure for a population”, Ecology, 48 (1967), 910–918 | DOI

[6] Denisov A. M., Makeev A. C., “Iteratsionnye metody resheniya obratnoi zadachi dlya odnoi modeli populyatsii”, Zh. vychisl. matem. i matem. fiz., 44:8 (2004), 1480–1489 | MR | Zbl

[7] Makeev A. C., “Metody resheniya obratnykh zadach dlya modeli populyatsii”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 2005, no. 3, 3–16 | MR | Zbl

[8] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1974 | MR