Analytical approximations and Padé approximants for Volterra’s population model. (English) Zbl 0953.92026

Summary: An analytic approximation for Volterra’s model for population growth of a species in a closed system is presented. The nonlinear integro-differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation. The series solution method and the decomposition method are implemented independently to the model and to a related ODE. The Padé approximants, that often show superior performance over series approximations, are effectively used in the analysis to capture the essential behavior of the population \(u(t)\) of identical individuals.


92D25 Population dynamics (general)
65R20 Numerical methods for integral equations
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[1] Scudo, F. M., Vito volterra and theoretical ecology, Theoret. Population Biol., 2, 1-23 (1971) · Zbl 0241.92001
[2] Small, R. D., Population growth in a closed model, Mathematical Modelling: Classroom Notes in Applied Mathematics (1989), SIAM: SIAM Boca Raton
[3] TeBeest, K. G., Numerical and analytical solutions of Volterra’s population model, SIAM Rev., 39, 3, 484-493 (1997) · Zbl 0892.92020
[4] Wazwaz, A. M.; Khuri, S. A., Two methods for solving integral equations, Appl. Math. Comput., 77, 79-89 (1996) · Zbl 0846.65077
[5] Wazwaz, A. M., A First Course in Integral Equations (1997), WSPC: WSPC Philadelphia, PA · Zbl 0924.45001
[6] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Singapore · Zbl 0802.65122
[7] Cherruault, Y.; Saccomandi, G.; Some, B., New results for convergence of Adomian’s method applied to integral equations, Math. Comput. Modelling, 16, 2, 85-93 (1992) · Zbl 0756.65083
[8] Burden, R. L.; Faires, J. D., Numerical Analysis (1993), Prindle, Weber & Schmidt: Prindle, Weber & Schmidt Boston · Zbl 0788.65001
[9] Baker, G. A.; Graves-Morris, P., Essentials of Padé Approximants (1996), Cambridge University Press: Cambridge University Press Boston · Zbl 0923.41001
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