Applications of Hes principles to partial differential equations

Applied Mathematics and Computation

Volumn 217, Issue 16, 2011, Pages 7039-7047

  Mohamad Jawad, Anwar Jaafar ^a   Petković, Marko D ^b   Biswas, Anjan ^c  

^a UNIVERSITY OF TECHNOLOGY   (Iraq)

^b UNIVERSITY OF NI   (Serbia)

^c DELAWARE STATE UNIVERSITY   (United States)

Author keywords

Burgers equation; Gas dynamics equation; Heat transfer equation; Peregrine equation; Semi inverse variational principle; Variational iteration method

Indexed keywords

BURGERS EQUATIONS; GAS DYNAMICS EQUATION; HEAT TRANSFER EQUATION; PEREGRINE EQUATION; SEMI-INVERSE VARIATIONAL PRINCIPLE; VARIATIONAL ITERATION METHOD;

DYNAMICS; GAS DYNAMICS; HEAT TRANSFER COEFFICIENTS; ITERATIVE METHODS; PARTIAL DIFFERENTIAL EQUATIONS; VARIATIONAL TECHNIQUES;

NONLINEAR EQUATIONS;

EID: 79952452222     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.02.013     Document Type: Article

References (30)

1. M.J. Ablowitz, and P.A. Clarkson Solitons and symmetries J. Eng. Math. 36 1-2 1999 1 9 (Pubitemid 30024285)
2. G. Adomian A review of the decomposition method in applied mathematics Math. Anal. Appl. 135 1988 501 544
3. D.A. Anderson, J.C. Tannehill, and R.H. Pletcher Computational Fluid Mechanics and Heat Transfer 1984 McGraw-Hill Company
4. N. Bildik, and A. Konuralp The Use of Variational Iteration Method, Differential Transform Method and Adomians Decomposition Method for Solving Different Types of Nonlinear Partial Differential Equations Int. J. Nonlinear Sci. Numer. Simul. 7 1 2006 65 70 (Pubitemid 43246582)
5. R.L. Burden, and J.D. Faires Numerical Analysis 1993 Boston PWS Publishing Company
6. D.J. Evans H. Bulut. A new approach to the gas dynamics equation, an application of the decomposition method Appl. Comput. Math. 79 7 2002 817 822 (Pubitemid 41710621)
7. D.D. Ganji, M. Nourollahi, and M. Rostamian A comparison of variational iteration method with adomians decomposition method in some highly nonlinear equations Int. J. Sci. Technol. 2 2 2007 179 188
8. C.S. Gardner, J.M. Green, M.D. Kruskal, and R.M. Miura Method for solving the Korteweg-de Vries equation Phys. Rev. Lett. 19 1967 1095 1097
9. L. Girgis, and A. Biswas Soliton perturbation theory for nonlinear wave equations Appl. Math. Comput. 216 7 2010 2226 2231
10. R. Hirota Exact solution of the Korteweg-de Vries equation for multiple collisions of Solitons Phys. Rev. Lett. 27 1971 1192 1194
11. J.H. He Variational iteration method-a kind of non-linear analytical technique: some examples Int. J. Nonlinear Mech. 34 4 1999 699 708
12. J.H. He Variational iteration method for autonomous ordinary differential systems Appl. Math. Comput. 114 2000 115 123
13. J.H. He The homotopy perturbation method for nonlinear oscillators with discontinuities Appl. Math. Comput. 151 2004 287 292
14. J.H. He Comparison of homotopy perturbation method and homotopy analysis method Appl. Math. Comput. 156 2004 527 539
15. J.H. He Asymptotology by homotopy perturbation method Appl. Math. Comput. 156 3 2004 591 596
16. J.H. He Homotopy perturbation method for bifurcation of nonlinear problems Int. J. Non-linear Sci. Numer. Simul. 6 2 2005 207 208
17. J.H. He Application of homotopy perturbation method to nonlinear wave equations Chaos, Solitons Fractals 26 2005 695 700
18. J.H. He Some asymptotic methods for strongly nonlinear equations Int. J. Modern Phys. B 10 06 2006 1141 1199
19. H. Jafari, M. Zabihi, and M. Saidy Application of homotopy-perturbation method for solving gas dynamics equation Appl. Math. Sci. 2 48 2008 2393 2396
20. J.H. He Approximate analytical solution for seepage flow with fractional derivatives in porous media Comput. Methods Appl. Mech. Eng. 167 1998 57 68
21. J.H. He Approximate solution of nonlinear differential equations with convolution product nonlinearities Comput. Methods Appl. Mech. Eng. 167 1998 69 73
22. J.H. He, and X.H. Wu Construction of solitary solution and compaction-like solution by variational iteration method Chaos Solitons Fractals 29 1 2006 108 113
23. V. Marinca An approximate solution for one-dimensional weakly nonlinear oscillation Int. J Non-linear Sci. Number Simul. 3 2002 107 110
24. P.J. Olver Applications of Lie Groups to Differential Equations 1986 Springer Berlin
25. M.F. Patricio, and P.M. Rosa The differential transform method for advection-diffusion problems Int. J. Comput. Math. Sci. 1 4 2007
26. C. Rogers, and W.F. Shadwick Bäcklund Transformations and their Application 1982 Academic Press New York
27. R. Sassaman, and A. Biswas Topological and non-topological solitons of nonlinear Klein-Gordon equations by Hes semi-inverse variational principle J. Franklin Inst. 347 7 2010 1148 1157
28. M.L. Wang Exact solutions for a compound KdV Burgers equation Phys. Lett. A 213 1996 279 287
29. A.M. Wazwaz New sets of solitary wave solutions to the KdV, mKdV and the generalized KdV equations Commun. Nonlinear Sci. Numer. Simul. 13 2 2008 331 339
30. A.M. Wazwaz Partial Differential Equations and Solitary Waves Theory 2010 Springer-Verlag New York, NY