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Variational iteration method for solving non-linear partial differential equations

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  • Hemeda, A.A.

Abstract

In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV–MKdV equation and Camassa–Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.

Suggested Citation

  • Hemeda, A.A., 2009. "Variational iteration method for solving non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1297-1303.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1297-1303
    DOI: 10.1016/j.chaos.2007.06.025
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    Cited by:

    1. Kaya, M.O. & Altay Demirbağ, S., 2009. "Application of parameter expansion method to the generalized nonlinear discontinuity equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1967-1973.

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