Solution of the prey and predator problem by homotopy perturbation method

Rafei, M.; Daniali, Hamid Reza Mohammadi; Ganji, D.D.; Pashaei, H.

doi:10.1016/j.amc.2006.11.007

Cited by 28 publications

(57 citation statements)

References 17 publications

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“…Foxes eat the rabbits and rabbits eat clover, and there is an increase and decrease in the number of foxes and rabbits [3,4,5,6,7]. Another example of the prey and predator problem is given in [15] in a lake there are two species of fish: A, which lives on plants of which there is a plentiful supply, and B (the predator) which subsists by eating A (the prey).…”

Section: The Prey and Predator Problemmentioning

confidence: 99%

“…Islam et al [1] used homotopy perturbation method to the Eq.(8). Moreover, Rafei et al [3,6] used both the variational iteration method to solve this problem.…”

Section: The Epidemic Modelmentioning

confidence: 99%

“…Moreover, Biazar et al [5] have successfully implemented the power series method to compute an approximation to the solution of the this problem. Moreover, the homotopy perturbation method is employed to find the approximate solution for this problem in [6]. In addition, the classical ADM is converted into a hybrid numeric-analytic method and applied to solve the prey and predator problem.…”

Section: The Prey and Predator Problemmentioning

confidence: 99%

“…Another example of the prey and predator problem is given in [15] in a lake there are two species of fish: A, which lives on plants of which there is a plentiful supply, and B (the predator) which subsists by eating A (the prey). For more details on the mathematical modeling leading to the following system of nonlinear equations, governing the problem; the readers can be found more details in [3,4,5,6,7,14,15,16].…”

Section: The Prey and Predator Problemmentioning

confidence: 99%

“…On the other hand, the problem in which some rabbits and foxes are considered living together, where foxes eat the rabbits and rabbits eat clover, and there is an increase and decrease in the number of foxes and rabbits appears to be interesting for the researchers to solve it and find the exact solution and approximate solutions to this problem, see for examples [3,4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

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A reliable iterative method for solving the epidemic model and the prey and predator problems

AL-Jawary

2014

IJBAS

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In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier as in Variational Iteration Method (VIM) and no needs to construct a homotopy as in Homotopy Perturbation Method (HPM). The results obtained are compared with the results by existing methods and prove that the presented method is very effective, simple and does not require any restrictive assumptions for nonlinear terms. The software used for the numerical calculations in this study was MATHEMATICA 8.0.

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Section: The Prey and Predator Problemmentioning

confidence: 99%

“…Islam et al [1] used homotopy perturbation method to the Eq.(8). Moreover, Rafei et al [3,6] used both the variational iteration method to solve this problem.…”

Section: The Epidemic Modelmentioning

confidence: 99%

Section: The Prey and Predator Problemmentioning

confidence: 99%

Section: The Prey and Predator Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A reliable iterative method for solving the epidemic model and the prey and predator problems

AL-Jawary

2014

IJBAS

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He's homotopy perturbation method for two‐dimensional heat conduction equation: Comparison with finite element method

Jalaal

Ganji

Mohammadi

2010

Heat Trans. Asian Res.

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Heat conduction appears in almost all natural and industrial processes. In the current study, a two-dimensional heat conduction equation with different complex Dirichlet boundary conditions has been studied. An analytical solution for the temperature distribution and gradient is derived using the homotopy perturbation method (HPM). Unlike most of previous studies in the field of analytical solution with homotopy-based methods which investigate the ODEs, we focus on the partial differential equation (PDE). Employing the Taylor series, the gained series has been converted to an exact expression describing the temperature distribution in the computational domain. Problems were also solved numerically employing the finite element method (FEM). Analytical and numerical results were compared with each other and excellent agreement was obtained. The present investigation shows the effectiveness of the HPM for the solution of PDEs and represents an exact solution for a practical problem. The mathematical procedure proves that the present mathematical method is much simpler than other analytical techniques due to using a combination of homotopy analysis and classic perturbation method. The current mathematical solution can be used in further analytical and numerical surveys as well as related natural and industrial applications even with complex boundary conditions as a simple accurate technique.

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New exact solutions for seventh-order Sawada-Kotera-Ito, Lax and Kaup-Kupershmidt equations using Exp-function method

Ganji

Davodi

Geraily

2009

Math. Meth. Appl. Sci.

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In this work, Exp-function method is used to solve three different seventh-order nonlinear partial differential KdV equations. Sawada-Kotera-Ito, Lax and Kaup-Kupershmidt equations are well known and considered for solve.Exp-function method can be used as an alternative to obtain analytic and approximate solutions of different types of differential equations applied in engineering mathematics. Ultimately this method is implemented to solve these equations and convenient and effective solutions are obtained.

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Solution of the prey and predator problem by homotopy perturbation method

Cited by 28 publications

References 17 publications

A reliable iterative method for solving the epidemic model and the prey and predator problems

A reliable iterative method for solving the epidemic model and the prey and predator problems

He's homotopy perturbation method for two‐dimensional heat conduction equation: Comparison with finite element method

New exact solutions for seventh-order Sawada-Kotera-Ito, Lax and Kaup-Kupershmidt equations using Exp-function method

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