Application of the decomposition method of adomian for solving the pantograph equation of order m

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 65, Issue 5, 2010, Pages 453-460

  Shakeri, Fatemeh ^a   Dehghan, Mehdi ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Adomian decomposition method; Delay differential equations; Pantograph equation of order m; Semi analytical approach

Indexed keywords

EID: 77955952732     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.1515/zna-2010-0510     Document Type: Article

References (44)

1. J.R. Ockendon and A.B. Taylor, Proc. Roy. Soc. London, Ser. A 322, 447 (1971).
2. C. T.H. Baker and E. Bukwwar, Elec. Transac. Numer. Anal. 11, 131 (2000).
3. Z. Fan, M. Z. Liu, and W. Cao, J. Math. Anal. Appl. 325, 1142 (2007).
4. N. Guglielmi and M. Zennaro, IMA J. Numer. Anal. 23, 421 (2003).
5. E. Ishiwata and Y. Muroya, Appl. Math. Comput. 187, 741 (2007).
6. T. Koto, Numer. Math. 84, 233 (1999).
7. D. S. Li and M. Z. Liu, J. Harbin-Inst. Tech. 32, 1 (2000).
8. M. Z. Liu and D. S. Li, Appl. Math. Comput. 155, 853 (2004).
9. M.Z. Liu, Z.W. Yang, and G.D. Hu, BIT 45, 743 (2005).
10. Y. Liu, Appl. Numer. Math. 24, 309 (1997).
11. A. Tamasan, Pure Math. Appl. 9, 215 (1998).
12. C. J. Zhang and G. Sun, J. Comput. Math. 22, 447 (2004).
13. J. J. Zhao, Y. Xu, H.X. Wang, and M. Z. Liu, Appl. Math. Comput. 181, 1170 (2006).
14. G. Adomian, J. Math. Anal. Appl. 135, 501 (1988).
15. G. Adomian and R. Rach, Nonlinear Analysis TMA 23, 615 (1994).
16. A. M. Wazwaz and A. Gorguis, Appl. Math. Comput. 154, 609 (2004).
17. A. M. Wazwaz, Bull. Inst. Math. Acad. Sinica 29, 125 (2001).
18. A. M. Wazwaz, Chaos, Solitons, and Fractals 12, 2283 (2001).
19. A. M. Wazwaz and S.A. Khuri, Appl. Math. Comput. 80, 287 (1996).
20. M. Dehghan, A. Hamidi, and M. Shakourifar, Appl. Math. Comput. 189, 1034 (2007).
21. T. Achouri and K. Omrani, Commun. Nonlinear Sci. Numer. Simul. 14, 2025 (2009).
22. E. Yee, Appl. Math. Comput. 56, 1 (1993).
23. M. Tatari and M. Dehghan, Phys. Scripta 72, 345 (2005).
24. D. Lesnic, Chaos, Solitons, and Fractals, 28, 776 (2006).
25. M. El-Shahed, J. Fract. Calc. 24, 23 (2003).
26. J. S. Kamdem and Z. Qiao, Chaos, Solitons, and Fractals, 31, 437 (2007).
27. K. Haldar, Appl. Math. Lett. 9, 109 (1996).
28. A. M. Wazwaz, Appl. Math. Comput. 166, 638 (2005).
29. D. Kaya and K. Al-Khaled, Phys. Lett. A 363, 433 (2007).
30. M. Dehghan and M. Tatari, Math. Prob. Eng. 2006, 1 (2006).
31. S. Momani and K. Al-Khaled, Appl. Math. Comput. 162, 1351 (2005).
32. M. Tatari and M. Dehghan, Math. Comput. Modelling, 45, 639 (2007).
33. M. Dehghan Int. J. Comput. Math. 81, 979 (2004).
34. N. Himoun, K. Abbaoui, and Y. Cherruault, Kybernetes 10, 423 (1999).
35. A. Saadatmandi and M. Dehghan, Z. Naturforsch. 64a, 783 (2009).
36. M. Tatari and M. Dehghan, Comput. Math. Appl. 58, 2160 (2009).
37. M. Dehghan and A. Saadatmandi, Chaos, Solitons, and Fractals 41, 1448 (2009).
38. F. Shakeri and M. Dehghan, Math. Comput. Modelling 48, 685 (2008).
39. A. Saadatmandi, M. Dehghan, and A. Eftekhari, Nonlinear Analysis: Real World Appl. 10, 1912 (2009).
40. M. Dehghan and F. Shakeri, Prog. Electromagn. Res. PIER 78, 361 (2008).
41. M. Dehghan, J. Manafian and A. Saadatmandi, Num. Met. Part. Diff. Eqs. 26, 448 (2010).
42. M. Dehghan, M. Shakourifar, and A. Hamidi, Chaos, Solitons, and Fractals 39, 2509 (2009).
43. M. Dehghan and F. Shakeri, Numer. Methods Part. Diff. Eqs. 25, 1238 (2009).
44. M. Dehghan and R. Salehi, Numer. Methods Part. Diff. Eqs. 26, 702 (2010).