×

New applications of variational iteration method. (English) Zbl 1084.35539

Summary: The variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled Schrödinger-KdV, generalized KdV and shallow water equations. The exact and numerical solutions obtained by the variational iteration method are compared with that obtained using Adomian decomposition method. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Drazin, P. G.; Johnson, R. S., Solutions: An Introduction (1989), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0661.35001
[2] Whitham, G. B., Linear Nonlinear Waves (1974), John Wiley and Sons: John Wiley and Sons California · Zbl 0373.76001
[3] Debtnath, L., Nonlinear Partial Differential Equations for Scientist and Engineers (1997), Birkhauser: Birkhauser Boston · Zbl 0892.35001
[4] Wazwaz, A. M., Partial Differential Equations Methods and Applications (2002), Rotterdam: Rotterdam Balkema · Zbl 0997.35083
[5] Hereman, W.; Banerjee, P. P.; Korpel, A.; Assnto, J.; Van Immerzeele, A.; Meerpoel, A., J. Phys. A: Math. Gen., 607 (1986) · Zbl 0621.35080
[6] Lei, Y.; Fajianj, Z.; Yinghai, W., Chaos Solitons Fractals, 13, 337 (2002)
[7] Hirota, R., Phys. Rev. Lett., 27, 1192 (1971) · Zbl 1168.35423
[8] A. Coely, et al. (Eds.), Backlund and Darboux Transformations, American Mathematical Society, Providence, Rhode Island, 2001.; A. Coely, et al. (Eds.), Backlund and Darboux Transformations, American Mathematical Society, Providence, Rhode Island, 2001.
[9] Malfeit, W., Am. J. Phys., 60, 650 (1992)
[10] Yan, C. T., Phys. Lett. A, 224, 77 (1996) · Zbl 1037.35504
[11] Wang, M. L., Phys. Lett. A, 215, 279 (1996)
[12] Yan, Z. Y.; Zhang, H. Q., J. Phys. A, 34, 1785 (2001) · Zbl 0970.35147
[13] Yan, Z. Y.; Zhang, H. Q., Appl. Math. Mech., 21, 382 (2000)
[14] Yan, Z. Y.; Zhang, H. Q., Phys. Lett. A, 285, 355 (2001) · Zbl 0969.76518
[15] Yan, Z. Y., Phys. Lett. A, 292, 100 (2001)
[16] Kaya, D., Commun. Nonlinear Sci. Numer. Simul., 10, 6, 693-702 (2005) · Zbl 1070.35061
[17] Kaya, D.; Elsayed, S. M., Phys. Lett. A., 313, 82 (2003) · Zbl 1040.35099
[18] Al-Khalled, K.; Allan, F., Math. Comput. Simul., 66, 6, 479-486 (2004) · Zbl 1113.65098
[19] He, J. H., Comput. Methods Appl. Mech. Eng., 167, 57-68 (1998) · Zbl 0942.76077
[20] He, J. H., Comput. Methods Appl. Mech. Eng., 167, 69-73 (1998) · Zbl 0932.65143
[21] He, J. H., Int. J. Nonlinear Mech., 34, 699-708 (1999) · Zbl 1342.34005
[22] He, J. H., Commun. Nonlinear Sci. Numer. Simul., 2, 4, 230-235 (1997)
[23] He, J. H., Appl. Math. Comput., 114, 2,3, 115-123 (2000) · Zbl 1027.34009
[24] Marinca, V., Int. J. Nonlinear Sci. Numer. Simul., 3, 107-120 (2002) · Zbl 1079.34028
[25] Draganescu, Gh. E.; Capalnasan, V., Int. J. Nonlinear Sci. Numer. Simul., 4, 219-226 (2004)
[26] Wazwaz, A. M., Computer and Mathematics with Application, 4, 1237-1244 (2001) · Zbl 0995.83051
[27] He, J. H., Approximate Analytical methods in Science and Engineering (2002), Henan Science and Technology Press: Henan Science and Technology Press Zhengzhou, (in Chinese) · Zbl 1021.34001
[28] He, J. H., Generalized Variational Principles in Fluids (2003), Science and Culture Publishing House of China: Science and Culture Publishing House of China Hongkong, (in Chinese) · Zbl 1054.76001
[29] Abdou, M. A.; Soliman, A. A., Variational iteration method for solving Burger’s and coupled Burger’s equations, J. Comput. Appl. Math., 181, 2, 245-251 (2005) · Zbl 1072.65127
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.