Laplace Adomian decomposition method for solving a fish farm model

M. Sambath; K. Balachandran

Nonautonomous Dynamical Systems (2016)

  • Volume: 3, Issue: 1, page 104-111
  • ISSN: 2353-0626

Abstract

top
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.

How to cite

top

M. Sambath, and K. Balachandran. "Laplace Adomian decomposition method for solving a fish farm model." Nonautonomous Dynamical Systems 3.1 (2016): 104-111. <http://eudml.org/doc/286775>.

@article{M2016,
abstract = {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.},
author = {M. Sambath, K. Balachandran},
journal = {Nonautonomous Dynamical Systems},
keywords = {Fish farm; Laplace decomposition method; Nonlinear differential equations; Adomian polynomials; nonlinear differential equations; Laplace transform method; Adomian decomposition method; fish farm model; numerical example},
language = {eng},
number = {1},
pages = {104-111},
title = {Laplace Adomian decomposition method for solving a fish farm model},
url = {http://eudml.org/doc/286775},
volume = {3},
year = {2016},
}

TY - JOUR
AU - M. Sambath
AU - K. Balachandran
TI - Laplace Adomian decomposition method for solving a fish farm model
JO - Nonautonomous Dynamical Systems
PY - 2016
VL - 3
IS - 1
SP - 104
EP - 111
AB - 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.
LA - eng
KW - Fish farm; Laplace decomposition method; Nonlinear differential equations; Adomian polynomials; nonlinear differential equations; Laplace transform method; Adomian decomposition method; fish farm model; numerical example
UR - http://eudml.org/doc/286775
ER -

References

top
  1. [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] Zbl0732.35003
  2. [2] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Dordrecht, 1994.  
  3. [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.  Zbl0645.92025
  4. [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] Zbl1186.65158
  5. [5] J. C. Butcher, Numerical methods for ordinary differential equations, Second edition, John Wiley & Sons, 2008.  Zbl1167.65041
  6. [6] S.N. Elgazery, Numerical solution for the Falkner-Skan equation, Chaos, Solitons and Fractals, 35 (2008) 738-746.  Zbl1135.76039
  7. [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. [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] Zbl1243.34100
  9. [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.  Zbl1156.92039
  10. [10] M. Hussain and M. Khan, Modified Laplace decomposition method, Appl. Math. Sci, 36 (2010) 1769-1783.  Zbl1208.35006
  11. [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. [12] S.A. Khuri, A Laplace decomposition algorithm applied to class of nonlinear differential equations, J Math. Appl, 4 (2001) 141-155.  Zbl0996.65068
  13. [13] S.A. Khuri, A new approach to Bratu’s problem, Appl. Math. Comput, 147 (2004) 131-136. [Crossref] Zbl1032.65084
  14. [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] Zbl1142.65058
  15. [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.  Zbl1217.65164
  16. [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. [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. [18] E. Yusufoglu, Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl. Math. Comput, 177 (2006) 572-580. [Crossref] Zbl1096.65067

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.