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A computational method for solution of the prey and predator problem. (English) Zbl 1060.65612

Summary: A mathematical model of the problem of prey and predator being presented and Adomian decomposition method is employed to compute an approximation to the solution of the system of nonlinear Volterra differential equations governing on the problem. Some plots for the population of the prey and predator versus time are presented to illustrate the solution.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
92D25 Population dynamics (general)
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References:

[1] Simmons, G. F., Differential Equations with Applications and Historical Notes (1972), McGraw-Hill · Zbl 0231.34001
[2] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordecht · Zbl 0802.65122
[3] Adomian, G.; Adomian, G. E., A global method for solution of complex systems, Math. Model, 5, 521-568 (1984) · Zbl 0556.93005
[4] Biazar, J.; Babolian, E.; Kember, G.; Nouri, A.; Islam, R., An alternate algorithm for computing Adomian polynomials, Appl. Math. Comput., 38, 2-3, 523-529 (2003) · Zbl 1027.65076
[5] Biazar, J.; Babolian, E.; Islam, R., Solution of systems of ordinary differential equations with Adomian decomposition method, Appl. Math. Comput., 147, 3, 713-719 (2004) · Zbl 1034.65053
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