Exact solutions of nonlinear diffusion equations by variational iteration method

Computers and Mathematics with Applications

Volumn 54, Issue 7-8, 2007, Pages 1112-1121

  Sadighi, A ^a   Ganji, D D ^a  

^a UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

Adomian decomposition method; Exact solution; Lagrange multipliers; Nonlinear diffusion equations; Variational iteration method

Indexed keywords

DIFFUSION; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; PERTURBATION TECHNIQUES; POLYNOMIALS;

ADOMIAN DECOMPOSITION METHOD; EXACT SOLUTION; VARIATIONAL ITERATION METHOD;

NONLINEAR EQUATIONS;

EID: 34748865368     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.077     Document Type: Article

References (26)

1. He J.H., and Wu X.-H. Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals 30 3 (2006) 700-708
2. J.H. He, M.A. Abdou, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals (in press)
3. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-Linear Mechanics 35 1 (2000) 37-43
4. He J.H. New interpretation of homotopy perturbation method. International Journal of Modern Physics B 20 18 (2006) 2561-2568
5. He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Applied Mathematics and Computation 135 1 (2003) 73-79
6. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Applied Mathematics and Computation 151 1 (2004) 287-292
7. He J.H. Periodic solutions and bifurcations of delay-differential equations. Physics Letters A 347 4-6 (2005) 228-230
8. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons and Fractals 26 3 (2005) 695-700
9. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons and Fractals 26 3 (2005) 827-833
10. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. International Journal of Nonlinear Science and Numerical Simulation 6 2 (2005) 207-208
11. He J.H. Homotopy perturbation method for solving boundary value problems. Physics Letters A 350 1-2 (2006) 87-88
12. He J.H. Variational iteration method - a kind of non-linear analytical technique: Some examples. International Journal of Non-Linear Mechanics 34 (1999) 699-708
13. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering 167 (1998) 57-68
14. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Computer Methods in Applied Mechanics and Engineering 167 (1998) 69-73
15. He J.H. Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computation 114 (2000) 115-123
16. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons and Fractals 29 (2006) 108-113
17. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 20 10 (2006) 1141-1199
18. He J.H. Non-perturbative Methods for Strongly Nonlinear Problems (2006), dissertation. de-Verlag im Internet GmbH, Berlin
19. Momani Sh., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos, Solitons and Fractals 27 (2006) 1119-1123
20. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 27-34
21. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 65-70
22. Wazwaz A.M. Exact solutions to nonlinear diffusion equations obtained by the decomposition method. Applied Mathematics and Computation 123 (2001) 109-122
23. Saeid E.A. The nonclassical solution of the inhomogeneous non-linear diffusion equation. Applied Mathematics and Computation 98 (1999) 103-108
24. Saeid E.A., and Hussein M.M. New classes of similarity solutions of the inhomogeneous nonlinear diffusion equations. Journal of Physics A 27 (1994) 4867-4874
25. Dresner L. Similarity Solutions of Nonlinear Partial Differential Equations (1983), Pitman, New York
26. Changzheng Q. Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method. IMA Journal of Applied Mathematics 62 (1999) 283-302