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Identifying an unknown function in a parabolic equation with overspecified data via He’s variational iteration method

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  • Dehghan, Mehdi
  • Tatari, Mehdi

Abstract

In this research, the He’s variational iteration technique is used for computing an unknown time-dependent parameter in an inverse quasilinear parabolic partial differential equation. Parabolic partial differential equations with overspecified data play a crucial role in applied mathematics and physics, as they appear in various engineering models. The He’s variational iteration method is an analytical procedure for finding solutions of differential equations, is based on the use of Lagrange multipliers for identification of an optimal value of a parameter in a functional. To show the efficiency of the new approach, several test problems are presented for one-, two- and three-dimensional cases.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:1:p:157-166
    DOI: 10.1016/j.chaos.2006.06.023
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2003. "Determination of a control function in three-dimensional parabolic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 89-100.
    2. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    3. Soliman, A.A., 2006. "A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 294-302.
    4. Abulwafa, E.M. & Abdou, M.A. & Mahmoud, A.A., 2006. "The solution of nonlinear coagulation problem with mass loss," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 313-330.
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    1. 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.

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