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Variational iteration method for one dimensional nonlinear thermoelasticity

Author

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  • Sweilam, N.H.
  • Khader, M.M.

Abstract

This paper applies the variational iteration method to solve the Cauchy problem arising in one dimensional nonlinear thermoelasticity. The advantage of this method is to overcome the difficulty of calculation of Adomian’s polynomials in the Adomian’s decomposition method. The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that the variational iteration method is a powerful mathematical tool for solving nonlinear problems.

Suggested Citation

  • Sweilam, N.H. & Khader, M.M., 2007. "Variational iteration method for one dimensional nonlinear thermoelasticity," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 145-149.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:145-149
    DOI: 10.1016/j.chaos.2005.11.028
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    Citations

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    Cited by:

    1. Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
    2. Khudhayr A. Rashedi & Musawa Yahya Almusawa & Hassan Almusawa & Tariq S. Alshammari & Adel Almarashi, 2025. "Fractional Dynamics: Applications of the Caputo Operator in Solving the Sawada–Kotera and Rosenau–Hyman Equations," Mathematics, MDPI, vol. 13(2), pages 1-23, January.
    3. Jamshad Ahmad & Syed Tauseef Mohyud-Din, 2014. "An Efficient Algorithm for Some Highly Nonlinear Fractional PDEs in Mathematical Physics," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-17, December.
    4. Ali, A.H.A. & Raslan, K.R., 2009. "Variational iteration method for solving partial differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1520-1529.
    5. Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
    6. Kumar, Rajneesh & Rupender,, 2009. "Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1619-1633.
    7. Darvishi, M.T. & Khani, F., 2009. "Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2484-2490.
    8. Assas, Laila M.B., 2008. "Variational iteration method for solving coupled-KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1225-1228.
    9. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.

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