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.
@article{bwmeta1.element.doi-10_1515_msds-2016-0006,
author = {M. Sambath and K. Balachandran},
title = {Laplace Adomian decomposition method for solving a fish farm model},
journal = {Nonautonomous Dynamical Systems},
volume = {3},
year = {2016},
pages = {104-111},
zbl = {1350.65076},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_msds-2016-0006}
}
M. Sambath; K. Balachandran. Laplace Adomian decomposition method for solving a fish farm model. Nonautonomous Dynamical Systems, Tome 3 (2016) pp. 104-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_msds-2016-0006/
[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] | Zbl 0732.35003
[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. | Zbl 0645.92025
[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] | Zbl 1186.65158
[5] J. C. Butcher, Numerical methods for ordinary differential equations, Second edition, John Wiley & Sons, 2008. | Zbl 1167.65041
[6] S.N. Elgazery, Numerical solution for the Falkner-Skan equation, Chaos, Solitons and Fractals, 35 (2008) 738-746. | Zbl 1135.76039
[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] | Zbl 1243.34100
[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. | Zbl 1156.92039
[10] M. Hussain and M. Khan, Modified Laplace decomposition method, Appl. Math. Sci, 36 (2010) 1769-1783. | Zbl 1208.35006
[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. | Zbl 0996.65068
[13] S.A. Khuri, A new approach to Bratu’s problem, Appl. Math. Comput, 147 (2004) 131-136. [Crossref] | Zbl 1032.65084
[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] | Zbl 1142.65058
[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. | Zbl 1217.65164
[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] | Zbl 1096.65067