Reduced polynomials and their generation in Adomian decomposition methods

CMES - Computer Modeling in Engineering and Sciences

Volumn 60, Issue 2, 2010, Pages 139-150

  Duan, Jun Sheng ^a   Guo, Ai Ping ^b  

^a SHANGHAI INSTITUTE OF TECHNOLOGY   (China)

^b BAOTOU TEACHERS COLLEGE   (China)

Author keywords

Adomian decomposition method; Adomian polynomials; Mathematica; Nonlinear operator; Reduced polynomials

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; ADOMIAN POLYNOMIALS; MATHEMATICA; NONLINEAR OPERATOR; REDUCED POLYNOMIALS;

MATHEMATICAL OPERATORS; OPERATIONS RESEARCH;

POLYNOMIALS;

EID: 77956114544     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. Abbaoui, K.; Cherruault, Y. (1994): Convergence of Adomian's method applied to differential equations. Comput. Math. Appl., vol. 28, pp. 103-109.
2. Abdelwahid, F. (2003): A mathematical model of Adomian polynomials. Appl. Math. Comput., vol. 141, pp. 447-453.
3. Adomian, G. (1986): Nonlinear Stochastic Operator Equations. Academic, Orlando.
4. Adomian, G. (1989): Nonlinear Stochastic Systems Theory and Applications to Physics. Kluwer Academic, Dordrecht.
5. Adomian, G. (1994): Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic, Dordrecht.
6. Azreg-Aïnou, M. (2009): A developed new algorithm for evaluating Adomian polynomials. CMES: Computer Modeling in Engineering & Sciences, vol. 42, no. 1, pp. 1-18.
7. Babolian, E.; Javadi, S. (2004): New method for calculating Adomian polynomials. Appl. Math. Comput., vol. 153, pp. 253-259.
8. Biazar, J.; Shafiof, S. M. (2007): A simple algorithm for calculating Adomian polynomials. Int. J. Contemp. Math. Sci., vol. 2, pp. 975-982.
9. Chen, W.; Lu, Z. (2004): An algorithm for Adomian decomposition method. Appl. Math. Comput., vol. 159, pp. 221-235.
10. Cherruault, Y. (1989): Convergence of Adomian's method. Kybernetes, vol. 18, pp. 31-38.
11. Choi, H. W.; Shin, J. G. (2003): Symbolic implementation of the algorithm for calculating Adomian polynomials. Appl. Math. Comput., vol. 146, pp. 257-271.
12. Gabet, L. (1994): The theoretical foundation of the Adomian method. Comput. Math. Appl., vol. 27, pp. 41-52.
13. Lai, H. Y.; Chen, C. K.; Hsu, J. C. (2008): Free vibration of non-uniform Euler-Bernoulli beams by the Adomian modified decomposition method. CMES: Computer Modeling in Engineering & Sciences, vol. 34, no. 1, pp. 87-116.
14. Pourdarvish, A. (2006): A reliable symbolic implementation of algorithm for calculating Adomian polynomials. Appl. Math. Comput., vol. 172, pp. 545-550.
15. Rach, R. (1984): A convenient computational form for the Adomian polynomials. J. Math. Anal. Appl., vol. 102, pp. 415-419.
16. Rach, R. (2008): A new definition of the Adomian polynomials. Kybernetes, vol. 37, pp. 910-955.
17. Rach, R.; Adomian, G.; Meyers, R. E. (1992): A modified decomposition. Comput. Math. Appl., vol. 23, pp. 17-23.
18. Soliman, A. A.; Abdou, M. A. (2008): The decomposition method for solving the coupled modified KdV equations. Math. Comput. Model., vol. 47, pp. 1035-1041.
19. Wazwaz, A. M. (1999): A reliable modification of Adomian decomposition method. Appl. Math. Comput., vol. 102, pp. 77-87.
20. Wazwaz, A. M. (2000): A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput., vol. 111, pp. 53-69.
21. Wazwaz, A. M. (2009): Partial Differential Equations and Solitary Waves Theory. Higher Education Press, Beijing.
22. Wazwaz, A. M.; El-Sayed, S. M. (2001): A new modification of the Adomian decomposition method for linear and nonlinear operators. Appl. Math. Comput., vol. 122, pp. 393-405.
23. Zhu, Y.; Chang, Q.; Wu, S. (2005): A new algorithm for calculating Adomian polynomials. Appl. Math. Comput., vol. 169, pp. 402-416.