Paper title: |
## On Calculation of Adomian Polynomials by MATLAB |

Published in: |
Issue 2, (Vol. 5) / 2011 |

Publishing date: |
2011-10-28 |

Pages: |
85-88 |

Author(s): |
FATOOREHCHI Hooman, ABOLGHASEMI Hossein |

Abstract. |
Adomian Decomposition Method (ADM) is an elegant technique to handle an extensive class of linear or nonlinear differential and integral equations. However, in case of nonlinear equations, ADM demands a special representation of each nonlinear term, namely, Adomian polynomials. The present paper introduces a novel MATLAB code which computes Adomian polynomials associated with several types of nonlinearities. The code exploits symbolic programming incorporated with a recently proposed alternative scheme to be straightforward and fast. For the sake of exemplification, Adomian polynomials of famous nonlinear operators, computed by the code, are given. |

Keywords: |
Adomian Decomposition, Adomian Polynomials, MATLAB, Nonlinear Functionals, Differential Equations |

References: | 1. G. Adomian, “A new approach to nonlinear partial differential equations,” J. Math. Anal. Appl., vol. 102, pp. 402-434, 1984. 2. Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994. 3. G. Adomian, “Solutions of nonlinear PDE,” Appl. Math. Lett., vol. 11(3), pp. 121-123, 1998. 4. J.-L. Li., “Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations,” J. Comput. Appl. Math., vol. 228, pp. 168-173, 2009. 5. K. Abbaoui, Y. Cherruault, “Convergence of Adomian’s Method Applied to Nonlinear Equations,” Mathl. Comput. Modeling, vol. 20(9), pp. 69-73, 1994. 6. Y-C. Jiao, C. Dang, Y. Yamamoto, “An extension of the decomposition method for solving nonlinear equations and its convergence,” Comput. Math. Appl., vol. 55, pp. 760-775, 2008. 7. S. Pamuk, “An application for linear and nonlinear heat equations by Adomian’s decomposition method,” Appl. Math. Comput., vol. 163, pp.89-96, 2005. 8. C. Arslanturk, “A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity,” Int. Comm. Heat Mass Tran., vol. 32, pp. 831- 841, 2005. 9. A. Wazwaz, A. Gorguis, “An analytic study of Fisher’s equation by using Adomian decomposition method,” Appl. Math. Comput., vol. 154, pp. 609-620, 2004. 10. B. Adjedj, “Application of the decomposition method to the understanding of HIV immune dynamics,” Kybernetes, vol. 28(3), pp. 271-283, 1999. 11. A. Wazwaz, Partial Differential Equations Method and Applications, Balkema Publishers, Abingdon, 2002. 12. H.-W. Choi, J.-G., “Symbolic implementation of the algorithm for calculating Adomian polynomials,” Appl. Math. Comput., vol. 146, pp. 257-271, 2003. 13. J. Biazar, M. Pourabd, “A Maple program for computing Adomian Polynomials,” International Mathematical Forum, vol. 1(39): 1919-1924, 2006. 14. J.-S. Duan, “Recurrence triangle for Adomian polynomials,” Appl. Math. Comput., vol. 216(4), pp. 1235-1241, 2010. 15. E. Babolian, Sh. Javadi, “New method for calculating Adomian polynomials,” Appl. Math. Comput., vol. 153, pp. 253-259, 2004. 16. J. Biazar, E. Babolian, G. Kember, A. Nouri, R. Islam, “An alternate algorithm for computing Adomian polynomials in special cases,” Appl. Math. Comput., vol. 138, pp. 523-529, 2003. 17. A. Wazwaz, “A new algorithm for calculating Adomian polynomials for nonlinear operators,” Appl. Math. Comput., vol. 111, pp. 53-69, 2000. |

Back to the journal content |