Üç Canlı Türünün Oluşturduğu Besin Zinciri Modelinin Varyasyonel İterasyon Ve Homotopi Pertürbasyon Yöntemi ile Çözümü

Year 2008, Volume: 8 Issue: 2, 27 - 36, 01.12.2008

Mehmet Merdan Tahir Khaniyev

Abstract

Keywords

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Üç Canlı Türünün Oluşturduğu Besin Zinciri Modelinin Varyasyonel İterasyon Ve Homotopi Pertürbasyon Yöntemi ile Çözümü

Abstract

Bu makalede, üç canlı türünün oluşturduğu besin zincri modeli gibi lineer olmayan adi diferensiyel denklem sistemlerinin yaklaşık analitik çözümlerini elde edebilmek için homotopy perturbation ve varyasyonel iterasyon yöntemleri uygulandı. Homotopy perturbation yöntemi varyasyonel iterasyon yöntemi ile mukayese edildi. Varyasyonel iterasyon yöntemi perturbation yöntemi olarak bilinen diğer non lineer yöntemlerden daha üstündür. Bu yöntemde genelde Lagrange çarpanları sistemler için düzeltme fonksiyoneli ile elde edildi. Çarpanlar varyasyonel teori ile belirlendi. Yöntemlerin doğruluğunu göstermek için birkaç tane grafik sunuldu

Keywords

Varyasyonel iterasyon yöntemi, Homotopy perturbation yöntemi, üç canlı türünün oluşturduğu besin zinciri modeli

References

• Rafei.M., Daniali. H., Ganji.D.D., Variational iteration method for solving the epidemic model and the prey and predator problem, Applied Mathematics and Computation, 186,1701–1709, (2007).
• Klebano. A., Hastings. A., Chaos in three species food chains, J Math Biol, 32,427– 451, (1994).
• He. J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-Linear Mech, 35, 37–43, (2000).
• Jordan. D.W., Smith P., Nonlinear Ordinary Differential University Press, (1999). thirded, Oxford
• Biazar J., Solution of the epidemic model by Adomian decomposition method, Applied Mathematics and Computation ,173, 1101– 1106, (2006).
• Chowdhury. MSH, I. Hashim. I., Application of homotopy-perturbation method to Klein– Gordon and sine-Gordon equations, Chaos Solitons & Fractals, in press.
• He. J.H., Homotopy perturbation method for solving boundary value problems, Phys Lett A ,350, 87–8, (2006).
• 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, 486– 491, (2005).
• He. J.H., A new approach to nonlinear partial differential equations, Communications in, Nonlinear Simulation, 2, 230–235, (1997). and Numerical equations with convolution
• He. J.H., Variational iteration method-a kind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics, 34, 699–708,(1999).
• He. J.H, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20, 1141– 1199, (2006).
• Abdou M.A., Soliman A.A., Variational- iteration method for solving Burger’s and coupled Burger’s equations, Journal of Computational and Applied Mathematics, 181, 245–251, (2005).
• He J.H., Homotopy perturbation method for solving boundary value problems, Phys Lett A, 350, 87–8, (2006).
• Soliman A.A., A numerical simulation and explicit solutions of KdV–Burgers’ and Lax’s Chaos,Solitons & Fractals, 29, 294–302, (2006). KdV equations,
• Gakkhar. S, Naji RK., Chaos in three species ratio dependent food chain, Chaos Solitons & Fractals, 14,771–778, (2002).
• J.H. He, Semi-inverse method of establishing generalized principles for fluid mechanics with aerodynamics, International Journal of Turbo Jet-Engines, 14, 23–28, (1997).
• Finlayson. B.A., The Method of Weighted Residuals Academic press, New York, (1972). Principles,
• He. J.H., Homotopy perturbation technique. Comput Methods Appl Mech Engrg, 62,257– 62, (1999).
• He. J.H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int J Non-linear Mech ,35, 37–43, (2000). 36
• Merdan,M., 2009. Homotopy Perturbation
• Method for Solving Human T-cell Lymphotropic
• Virus I(HTLV-I) Infection of CD4+ T-cells
• Model, Mathematical and Computation
• Applications;14(2), 85-96.