Variational iteration method for one dimensional nonlinear thermoelasticity

Chaos, Solitons and Fractals

Volumn 32, Issue 1, 2007, Pages 145-149

  Sweilam, N H ^a   Khader, M M ^b  

^a CAIRO UNIVERSITY   (Egypt)

^b BENHA UNIVERSITY   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; POLYNOMIALS; PROBLEM SOLVING;

ADOMIAN'S DECOMPOSITION; CAUCHY PROBLEM; NONLINEAR PROBLEMS; VARIATIONAL ITERATION METHOD;

THERMOELASTICITY;

EID: 33748578650     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.11.028     Document Type: Article

References (20)

1. Abulwafa EM, Abdou MA, Mahmoud AA. The solution of nonlinear coagulation problem with mass loss. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2005.08.044, in press.
2. 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
3. Dra ̌ga ̌nnescu GhE., Cofan N., and Rujan D.L. Nonlinear vibrations a nano sized sensor with fractional damping. J Optoelectron Adv Mater 7 2 (2005) 877-884
4. Dra ̌ga ̌nnescu GhE., and Ca ̌pa ̌lna ̌san V. Nonlinear relaxation phenomena in polycrystalline solids. Int J Nonlinear Sci Numer Simulat 4 (2003) 219-225
5. Jiang S., and Bonn. Numerical solution for the Cauchy problem in nonlinear 1-D-thermoelasticity. Computing 44 (1990) 147-158
6. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Methods Appl Mech Eng 167 1-2 (1998) 57-68
7. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput Methods Appl Mech Eng 167 1-2 (1998) 69-73
8. He J.H. Variational iteration method-a kind of non-linear analytical technique: some examples. Int J Non-Linear Mech 34 (1999) 699-708
9. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl Math Comput 114 2-3 (2000) 115-123
10. He J.H. A simple perturbation approach to Blasius equation. Appl Math Comput 140 2-3 (2003) 217-222
11. He J.H., Wan Y.Q., and Guo Q. An iteration formulation for normalized diode characteristics. Int J Circ Theory Appl 32 6 (2004) 629-632
12. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons & Fractals 19 4 (2004) 847-851
13. He J.H. A generalized variational principle in micromorphic thermoelasticity. Mech Res Commun 32 1 (2005) 93-98
14. Liu H.M. Variational approach to nonlinear electrochemical system. Int J Nonlinear Sci Numer Simulat 5 1 (2004) 95-96
15. Liu H.M. Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Chaos, Solitons & Fractals 23 2 (2005) 573-576
16. Moura D.C.A. A linear uncoupling numerical scheme for the nonlinear coupled thermodynamics equations. In: Pereyra V., and Reinoze A. (Eds). Lecture Notes in Mathematics 1005 (1983), Berlin-Springer 204-211
17. Momani S., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals 27 5 (2006) 1119-1123
18. Slemrod M. Global existence, uniqueness and asymptotic stability of classical solutions in one-dimensional non-linear thermoelasticity. Arch Rat Anal 76 2 (1981) 97-134
19. Soliman AA. A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2005.08.054, in press.
20. Wazwaz A.M. A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems. Comput Math Appl 41 (2001) 1237-1244