Laplace Adomian decomposition method for solving a fish farm model

• Autorzy: M. Sambath , K. Balachandran
• Języki publikacji: EN

Abstrakty

EN

In this work, a combined form of the Laplace transform method and the Adomian decomposition method is implemented to give an approximate solution of nonlinear systems of differential equations such as fish farm model with three components nutrient, fish and mussel. The technique is described and illustrated with a numerical example.

Słowa kluczowe

EN

Fish farm; Laplace decomposition method; Nonlinear differential equations; Adomian polynomials

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 104-111

Daty

otrzymano

2016-04-21

zaakceptowano

2016-08-15

online

2016-09-12

Twórcy

autor

M. Sambath

• Department of Mathematics, Periyar University, Salem-636011, India

autor

K. Balachandran

• Department of Mathematics, Bharathiar University, Coimbatore-641046, India

Bibliografia

• [1] G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Comput. Math. Appl, 21 (5) (1991) 101-127. [Crossref]
• [2] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Dordrecht, 1994.
• [3] A. Ardito, S. de Gregorio, L. Lamberti, P. Ricciardi, Dynamics of a lake ecosystem, in L.M. Ricciardi (Ed.), Biomathematics and Related Computational Problems, (1988) 111-119.
• [4] D. Bahuguna, A. Ujlayan and D.N. Pandeya, A comparative study of numerical methods for solving an integro-differential equation,Comput. Math. Appl, 57 (2009) 1485-1493. [WoS][Crossref]
• [5] J. C. Butcher, Numerical methods for ordinary differential equations, Second edition, John Wiley & Sons, 2008.
• [6] S.N. Elgazery, Numerical solution for the Falkner-Skan equation, Chaos, Solitons and Fractals, 35 (2008) 738-746.
• [7] J. Fadaei and M. M. Moghadam, Numerical Solution of Systems of Integral Differential Equations by Using Modified Laplace- Adomian Decomposition Method, World Applied Sciences Journal 19 (2012) 1818-1822.
• [8] N.H. Gazi, Dynamics of populations in fish farm: Analysis of stability and direction of Hopf-bifurcating periodic oscillation, Appl. Math Modell, 36 (2012) 2118-2127. [WoS][Crossref]
• [9] N.H. Gazi, S.R. Khan and C.G. Chakrabarti, Integration of mussel in fish farm: Mathematical model and analysis, Nonlinear Analysis:Hybrid Systems, 3 (2009)74-86.
• [10] M. Hussain and M. Khan, Modified Laplace decomposition method, Appl. Math. Sci, 36 (2010) 1769-1783.
• [11] Y. Khan, An effective modification of the Laplace decomposition method for nonlinear equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009) 1373-1376.
• [12] S.A. Khuri, A Laplace decomposition algorithm applied to class of nonlinear differential equations, J Math. Appl, 4 (2001) 141-155.
• [13] S.A. Khuri, A new approach to Bratu’s problem, Appl. Math. Comput, 147 (2004) 131-136. [Crossref]
• [14] S.Momani and V.S. Erturk, Solutions of non-linear oscillators by the modified differential transform method, Comput.Math. Appl, 55 (2008) 833-842. [Crossref][WoS]
• [15] M.Y. Ongun, The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4+T cells, Math. Comp. Modell, 53 (2011) 597-603.
• [16] H. Pad´e, Sur la repr´esentation approch´ee d’une fonction par des fractions rationnelles, Ann. Sci. ´Ec. Norm. Sup., 9 (1892) 1-93.
• [17] F. Saei, F. Dastmalchi, D. Misagh, Y. Zahiri, M. Mahmoudi, V. Salehian, and N. Rafati Maleki, New Application of Laplace Decomposition Algorithm For Quadrtic Riccati Differential Equation by Using Adomian’s Polynomials, Life Science Journal, 10 (2013) 3s.
• [18] E. Yusufoglu, Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl. Math. Comput, 177 (2006) 572-580. [Crossref]

Identyfikatory

DOI

10.1515/msds-2016-0006