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Adomian Decomposition Method for Solving Ratio-Dependent Prey-Predator System with Harvesting on Predator

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Abstract:

In this article, Adomian Decomposition Method is used to find out the approximate solution of ratio-dependent prey-predator model with predator harvesting. The significance of ADM over other numerical discretization techniques is that it has the eminence to solve problems directly with no un-physical restrictive assumptions such as linearization, per-turbation, massive computation and any other transformation. ADM solves the problem and arrives at the approximate solution in the form of series with solution components that are easily computable. It requires very less work in comparison with other traditional methods. The graphical representations of prey and predator population contrasted with time are drawn to examine the performance and reliability of this technique.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 15)
Pages:
36-42
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.15.36
Citation:
V. Madhusudanan et al., "Adomian Decomposition Method for Solving Ratio-Dependent Prey-Predator System with Harvesting on Predator", Bulletin of Mathematical Sciences and Applications, Vol. 15, pp. 36-42, 2016
Online since:
May 2016
Authors:
V. Madhusudanan, P.N. Duraiswamy, S. Vijaya
Keywords:
Adomian Decomposition Method, Predator Harvesting, Ratio-Dependent Prey-Predator Model
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Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] Abdoul R. Ghotbi,A. Barari and D. D. Ganji, Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method, Hindawi Publishing Corporation , Volume 2008, Article ID 945420, 8 pages, doi: 10. 1155/2008/945420.

DOI: https://doi.org/10.1155/2008/945420

[2] D.K. Arrowsmith, C.M. Place, Ordinary Differential Equations, Chapman and Hall, (1982).

[3] Francisco J. Solis. Self –limitation in a discrete predator-prey model, Mathematical and Computer Modelling, 48, 2008, (1-2) : pp.191-196.

DOI: https://doi.org/10.1016/j.mcm.2007.09.006

[4] G. Adomian, A global method for solution of complex systems , Math. Model 5 (1984) 521-568.

[5] G. Adomian, Solving Frontier Problems of Physics : The Decomposition Method, Kluwer Academic Publishers, Dordecht, (1994).

[6] J. Biazar and R. Montazeri, A Computational method for solution of the prey and predator problem, Applied Mathematics and Computation , 163, 2005, (2): pp.841-847.

DOI: https://doi.org/10.1016/j.amc.2004.05.001

[7] J.D. Murray, Mathematical Biology: I. An Introduction, Springer, Berlin, (2002).

[8] K. Abboui,Y. Cherruault, New ideas for proving convergence of decomposition methods, Comput. Appl. Math . 29 (7) (1995) 103-105.

[9] Lazhar Bougoffa, Solvability of the predator and prey system with variable coefficients and comparison of the results with modified decomposition, Applied Mathematics and Computation, 182, 2006, (1): pp.383-387.

DOI: https://doi.org/10.1016/j.amc.2006.02.050

[10] M.S.H. Chowdhury, I. Hashim and S. Mawa, Solution of prey predator problem by numeric analytic technique, Communications in Nonlinear Science and Numerical Simulation , 14 , 2009, (4): pp.1008-1012.

DOI: https://doi.org/10.1016/j.cnsns.2007.11.006

[11] O. D. Makinde, Solving ratio-dependent predator-prey system with constant effort harvesting using Adomian decomposition method, Applied Mathematics and Computation, vol. 186, no. 1, p.17–22, (2007).

DOI: https://doi.org/10.1016/j.amc.2006.07.083

[12] Safar Irandoust, Ahmad Golbabai, Hosein Kheiri and Davood Ahmadian, Homotopy analysis method for solving ratio-dependent predator-prey system with constant effort harvesting by using two parameters h1 and h2, Acta Universitatis Apulensis , 2011, 327-340.

[13] V. Daftardar-Gejji ,H. Jafari , Adomian decomposition a tool for solving a system of fractional differential equation ,J. Math . Anal. Appl. 301 (2) (2005) 508-518.

DOI: https://doi.org/10.1016/j.jmaa.2004.07.039
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