×
Rafei, M.; Daniali, H.; Ganji, D. D.; Pashaei, H.

Solution of the prey and predator problem by homotopy perturbation method. (English) Zbl 1119.65063

Appl. Math. Comput. 188, No. 2, 1419-1425 (2007).
Summary: The problem of prey and predator is presented and the homotopy perturbation method is employed to compute an approximation to the solution of the system of nonlinear Volterra differential equations governing on the problem. The results are compared with the results using the Adomian decomposition and the power series methods. Some plots are presented to show the populations of the prey and the predator versus time for illustrating the reliability and simplicity of the method.

Cited in 4 Documents

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

homotopy perturbation method; system of nonlinear differential equations; prey and predator problem; numerical examples; Adomian decomposition; power series methods
PDF BibTeX XML Cite
\textit{M. Rafei} et al., Appl. Math. Comput. 188, No. 2, 1419--1425 (2007; Zbl 1119.65063)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Simmons, G.F., Differential equations with applications and historical notes, (1972), McGraw-Hill · Zbl 0231.34001
[2] Biazar, J.; Montazeri, R., A computational method for solution of the prey and predator problem, Applied mathematics and computation, 163, 2, 841-847, (2005) · Zbl 1060.65612
[3] Biazar, J.; Ilie, M.; Khoshkenar, A., A new approach to the solution of the prey and predator problem and comparison of the results with the Adomian method, Applied mathematics and computation, 171, 1, 486-491, (2005) · Zbl 1084.65068
[4] He, J.H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied mathematics and computation, 151, 1, 287-292, (2004) · Zbl 1039.65052
[5] He, J.H., Comparison of homotopy perturbation method and homotopy analysis method, Applied mathematics and computation, 156, 2, 527-539, (2004) · Zbl 1062.65074
[6] He, J.H., Asymptotology by homotopy perturbation method, Applied mathematics and computation, 156, 3, 591-596, (2004) · Zbl 1061.65040
[7] He, J.H., Homotopy perturbation method for bifurcation of nonlinear problems, International journal of non-linear sciences and numerical simulation, 6, 2, 207-208, (2005) · Zbl 1401.65085
[8] He, J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos, solitons & fractals, 26, 3, 695-700, (2005) · Zbl 1072.35502
[9] He, J.H., Limit cycle and bifurcation of nonlinear problems, Chaos, solitons & fractals, 26, 3, 827-833, (2005) · Zbl 1093.34520
[10] He, J.H., Homotopy perturbation method for solving boundary value problems, Physics letters A, 350, 1-2, 87-88, (2006) · Zbl 1195.65207
[11] He, J.H., Some asymptotic methods for strongly nonlinear equations, International journal of modern physics B, 20, 10, 1141-1199, (2006) · Zbl 1102.34039
[12] He, J.H., Homotopy perturbation technique, Computer methods in applied mechanics and engineering, 178, 3-4, 257-262, (1999) · Zbl 0956.70017
[13] Rafei, M.; Ganji, D.D., Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method, International journal of nonlinear sciences and numerical simulation, 7, 3, 321-329, (2006) · Zbl 1160.35517
[14] Ganji, D.D.; Rafei, M., Solitary wave solutions for a generalized hirota – satsuma coupled KdV equation by homotopy perturbation method, Physics letters A, 356, 2, 131-137, (2006) · Zbl 1160.35517
[15] Siddiqui, A.M.; Mahmood, R.; Ghori, Q.K., Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Physics letters A, 352, 4-5, 404-410, (2006) · Zbl 1187.76622
[16] Abbasbandy, S., Homotopy perturbation method for quadratic Riccati differential equation and comparison with adomian’s decomposition method, Applied mathematics and computation, 172, 1, 485-490, (2006) · Zbl 1088.65063
[17] Abbasbandy, S., Iterated he’s homotopy perturbation method for quadratic Riccati differential equation, Applied mathematics and computation, 175, 1, 581-589, (2006) · Zbl 1089.65072
[18] Abbasbandy, S., Numerical solutions of the integral equations: homotopy perturbation method and adomian’s decomposition method, Applied mathematics and computation, 173, 1, 493-500, (2006) · Zbl 1090.65143
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.