Homotopy perturbation method for solving partial differential equations

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 64, Issue 3-4, 2009, Pages 157-170

  Mohyud Din, Syed Tauseef ^a   Noor, Muhammad Aslam ^a  

^a COMSATS Institute of Information Technology ^*  (Pakistan)

Author keywords

Boussinesq equations; Fisher's equations; Helmholtz equations; Homotopy perturbation method; Initial boundary value problems; Partial differential equations

Indexed keywords

EID: 68949146686     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.1515/zna-2009-3-402     Document Type: Article

References (65)

1. A. Ghorbani and J. S. Nadjfi, Int. J. Nonlinear Sci. Numer. Simul. 8, 229 (2007).
2. A. Ghorbani, Chaos, Solitons and Fractals (2007), in press.
3. J.H. He, Phys. Lett. A 350, 87 (2006).
4. J.H. He, Appl. Math. Comput. 156, 527 (2004).
5. J.H. He, Int. J. Nonlinear Sci. Numer. Simul. 6, 207 (2005).
6. J.H. He, Appl. Math. Comput. 151, 287 (2004).
7. J.H. He, Int. J. Nonlinear Mech. 35, 115 (2000).
8. J.H. He, Int. J. Mod. Phys. 20, 1144 (2006).
9. S. T. Mohyud-Din and M.A. Noor, Math. Prob. Eng., 1 (2007).
10. M.A. Noor and S. T. Mohyud-Din, Math. Comput. Modl. 45, 954 (2007).
11. M.A. Noor and S.T. Mohyud-Din, Comput. Math. Appl. 55, 2953 (2008).
12. M.A. Noor and S. T. Mohyud-Din, J. Math. Anal. Appl. Th. 1, 161 (2006).
13. M.A. Noor and S. T. Mohyud-Din, Int. J. Math. Comput. Sci. 2, 345 (2007).
14. M.A. Noor and S. T. Mohyud-Din, Int. J. Mod. Math. (2008), in press.
15. M.A. Noor and S. T. Mohyud-Din, Int. J. Nonlinear Sci. Numer. Simul. 9, 141 (2008).
16. M.A. Noor and S. T. Mohyud-Din, Math. Prob. Eng. (2008), in press.
17. M.A. Noor and S.T. Mohyud-Din, Comput. Math. Appl. (2008), in press.
18. M.A. Noor and S. T. Mohyud-Din, J. Appl. Math. Comput. 29, 81 (2009).
19. L. Xu, Comput. Math. Appl. 54, 1067 (2007).
20. S. Abbasbandy, J. Comput. Appl. Math. 207, 59 (2007).
21. M.A. Abdou and A.A. Soliman, Physica D 211, 1 (2005).
22. J.H. He, J. Comput. Appl. Math. 207, 3 (2007).
23. J.H. He and X. Wu, Comput. Math. Appl. 54, 881 (2007).
24. J.H. He, Int. J. Nonlinear Mech. 34, 699 (1999).
25. J.H. He, Phys. Scr. 76, 680 (2007).
26. S. T. Mohyud-Din, J. Appl. Math. Comput. (2008), in press.
27. S. T. Mohyud-Din, A reliable algorithm for Blasius equation, Proceedings of the International Conference on Mathematical Sciences, Selangor, Malaysia 2007, pp. 616 - 626.
28. M.A. Noor and S. T. Mohyud-Din, Appl. Math. Comput. 189, 1929 (2007).
29. M.A. Noor and S. T. Mohyud-Din, Comput. Math. Appl. 54, 1101 (2007).
30. M.A. Noor and S. T. Mohyud-Din, J. Appl. Math. Comput. (2008), in press.
31. M.A. Noor, S. T. Mohyud-Din, and M. Tahir, Diff. Eqns. Nonlin. Mech. (2007), in press.
32. M.A. Noor and S. T. Mohyud-Din, Int. J. Appl. Math. Eng. Sci. (2008), in press.
33. M.A. Haji and K. Al-Khaled, Appl. Math. Comput. 191, 320 (2007).
34. A. M. Wazwaz and A. Gorguis, Appl. Math. Comput. 47, 609 (2004).
35. A. M. Wazwaz, Chaos, Solitons and Fractals 12, 1549 (2001).
36. A. M. Wazwaz, Comput. Math. Appl. 54, 933 (2007).
37. A. M. Wazwaz, Comput. Math. Appl. 54, 895, 902 (2007).
38. A. M. Wazwaz, Appl. Math. Comput. 123, 219 (2001).
39. A. M. Wazwaz, Int. J. Comput. Math. 76, 159 (1999).
40. M.A. Noor, S.T. Mohyud-Din, and A. Waheed, J. Appl. Math. Comput. 29, 1 (2008).
41. M.A. Noor, S. T. Mohyud-Din, and A. Waheed, Acta Applnda. Mathmtce. (2008), in press.
42. M.A. Noor, S. T. Mohyud-Din, and A. Waheed, Appl. Math. Inf. Sci. 2, 135 (2008).
43. M.A. Noor, K. I. Noor, S. T. Mohyud-Din, and A. Shabir, Appl. Math. Comput. 183, 1249 (2006).
44. M.A. Noor and S. T. Mohyud-Din, J. Math. Math. Sci. 1, 9 (2007).
45. S.D. Conte, J. Assoc. Comput. Mach. 4, 210 (1957).
46. S.D. Conte and W.C. Royster, Prox. Am. Math. Soc. 7, 742 (1956).
47. L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhauser, Boston 1997.
48. D. J. Evans, Comput. J. 8, 280 (1965).
49. D. J. Evans andW. S. Yousef, Int. J. Comput. Math. 40, 93 (1991).
50. L. Edelstein-Keshet, Mathematical Models in Biology, McGraw-Hill, New York 1987.
51. S. M. El-Sayad and D. Kaya, Appl. Math. Comput. 157, 523 (2004).
52. S. M. El-Sayed and D. Kaya, Appl. Math. Comput. 150, 763 (2004).
53. Z. Feng, Wave Motion 37, 17 (2003).
54. S. Iyanaga, and Y. Kawada, Encyclopedia Dictionary of Mathematics, MIT Press, Cambridge, MA 1962.
55. T. Kawahara and M. Tanaka, Phys. Lett. A 97, 311 (1983).
56. J.D. Logan, An Introduction to Nonlinear Partial Differential Equations, Wiley-Interscience, New York 1994.
57. C. Lubich and A. Ostermann, BIT 27, 216 (1987).
58. A. R. Manwell, The Tricomi Equations with Applications to the Theory of Plane Transonic Flow, Pitman, London, UK 1979.
59. J.W. Miller, SIAM J. Math. Anal. 4, 314 (1973).
60. J.D. Murray, Mathematical Biology, Springer-Verlag, Berlin 1989.
61. W. Malfliet, Am. J. Phys. 60, 1032 (1992).
62. R. E. Mickens, Comput. Math. Appl. 45, 429 (2003).
63. J. Smollet, Shock Waves and Reaction Diffusion Equations, Springer-Verlag, New York 1983.
64. S. Vandewalle and R. Piessens, Appl. Numer. Math. 8, 149 (1991).
65. X.Y. Wang, Phys. Lett. A 131, 277 (1988).