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Variational iteration method for solving the wave equation subject to an integral conservation condition

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  • Dehghan, Mehdi
  • Saadatmandi, Abbas

Abstract

In this work, the well known variational iteration method is used for solving the one-dimensional wave equation that combines classical and integral boundary conditions. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which tends to the exact solution of the problem. We will change the main problem to a direct problem which is easy to handle the variational iteration method. Illustrative examples are included to demonstrate the validity and applicability of the presented method.

Suggested Citation

  • Dehghan, Mehdi & Saadatmandi, Abbas, 2009. "Variational iteration method for solving the wave equation subject to an integral conservation condition," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1448-1453.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1448-1453
    DOI: 10.1016/j.chaos.2008.06.009
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2007. "The one-dimensional heat equation subject to a boundary integral specification," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 661-675.
    2. Tatari, Mehdi & Dehghan, Mehdi, 2007. "He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 671-677.
    3. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
    4. Said Mesloub & Abdelfatah Bouziani, 1999. "On a class of singular hyperbolic equation with a weighted integral condition," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-9, January.
    5. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    6. Dehghan, Mehdi & Tatari, Mehdi, 2008. "Identifying an unknown function in a parabolic equation with overspecified data via He’s variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 157-166.
    7. Abdelfatah Bouziani, 2002. "Initial-boundary value problem with a nonlocal condition for a viscosity equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-12, January.
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    Cited by:

    1. Chein-Shan Liu & Chih-Wen Chang & Yung-Wei Chen & Jian-Hung Shen, 2022. "To Solve Forward and Backward Nonlocal Wave Problems with Pascal Bases Automatically Satisfying the Specified Conditions," Mathematics, MDPI, vol. 10(17), pages 1-16, August.

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