Toward a modified variational iteration method

Journal of Computational and Applied Mathematics

Volumn 207, Issue 1, 2007, Pages 137-147

  Abassy, Tamer A ^a   El Tawil, Magdy A ^b   El Zoheiry, H ^b  

^a BENHA UNIVERSITY   (Egypt)

^b CAIRO UNIVERSITY   (Egypt)

Author keywords

Adomian decomposition method; Analytical solution; Burgers' equation; KdV equation; Nonlinear partial differential equation; Variational iteration method

Indexed keywords

DIFFERENTIAL EQUATIONS; DOMAIN DECOMPOSITION METHODS; NONLINEAR EQUATIONS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

ADOMIAN DECOMPOSITION METHOD; ANALYTICAL SOLUTION; BURGERS' EQUATION; KDV EQUATION; NONLINEAR PARTIAL DIFFERENTIAL EQUATION; VARIATIONAL ITERATION METHOD (VIM);

ITERATIVE METHODS;

EID: 34250678087     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.07.019     Document Type: Article

References (15)

1. Abassy T.A., El-Tawil M., and Kamel H. The solution of KdV and mKdV equations using Adomian Padé approximation. Int. J. Nonlinear Sci. Numer. Simulation 5 4 (2004) 327-339
2. T.A. Abassy, M. El-Tawil, H. Kamel, The solution of Burgers' and good Boussinesq equations using ADM-Padé technique, Chaos, Solitons & Fractals, in press.
3. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burger's and coupled Burger's equations. J. Comput. Appl. Math. 181 2 (2005) 245-251
4. EL-Sayed S.M., and Kaya D. An application of the ADM to seven-order Sawada-Kotara equations. Appl. Math. Comput. 157 (2004) 93-101
5. He J.H. A new approach to nonlinear partial differential equations. Commun. Nonlinear Sci. Numer. Simulation 2 4 (1997) 230-235
6. He J.H. Variational iteration method-a kind of non-linear analytical technique: some examples. Int. J. Non-Linear Mech. 34 4 (1999) 699-708
7. He J.H. Approximate analytical solution of Blasius' equation. Commun. Nonlinear Sci. Numer. Simulation 4 1 (1999) 75-78
8. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 2-3 (2000) 115-123
9. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 10 (2006) 1141-1199
10. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons & Fractals 29 1 (2006) 108-113
11. xx. Comm. Pure Appl. Math. 3 (1950) 201-230
12. Inokuti M., Sekine H., and Mura T. General use of the Lagrange multiplier in non-linear mathematical physics. In: Nemat-Nasser S. (Ed). Variational Method in the Mechanics of Solids (1978), Pergamon Press, Oxford 156-162
13. Marinca V. An approximate solution for one-dimensional weakly nonlinear oscillations. Int. J. Nonlinear Sci. Numer. Simulation 3 (2002) 107-120
14. Soliman A.A. Numerical simulation of the generalized regularized long wave equation by He's variational iteration method. Math. Comput. Simulation 70 2 (2005) 119-124
15. Soliman A.A. A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations. Chaos, Solitons & Fractals 29 2 (2006) 294-302