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Iterative Solution of a Nonlinear Static Beam Equation

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Ukrainian Mathematical Journal Aims and scope

We consider a boundary-value problem for the nonlinear integrodifferential equation

$$ {u}^{\prime \prime \prime \prime }-m\left(\underset{0}{\overset{l}{\int }}{u}^{\prime 2} dx\right){u}^{{\prime\prime} }=f\left(x,u,{u}^{\prime}\right),\kern1em m(z)\ge \upalpha >0,\kern1em 0\le z<\infty, $$

simulating the static state of the Kirchhoff beam. The problem is reduced to a nonlinear integral equation, which is solved by using the Picard iterative method. The convergence of the iterative process is established and the error is estimated.

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Authors and Affiliations

  1. Georgian Technical University, Tbilisi, Georgia

    G. Berikelashvili & J. Peradze

  2. A. Razmadze Mathematical Institute, Tbilisi, Georgia

    G. Berikelashvili

  3. I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    A. Papukashvili & J. Peradze

  4. I. Vekua Institute of Applied Mathematics, Tbilisi, Georgia

    A. Papukashvili

Authors
  1. G. Berikelashvili
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  2. A. Papukashvili
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  3. J. Peradze
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Corresponding author

Correspondence to J. Peradze.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 8, pp. 1024–1033, August, 2020. Ukrainian DOI: 10.37863/umzh.v72i8.833.

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Berikelashvili, G., Papukashvili, A. & Peradze, J. Iterative Solution of a Nonlinear Static Beam Equation. Ukr Math J 72, 1185–1196 (2021). https://doi.org/10.1007/s11253-020-01858-y

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  • DOI: https://doi.org/10.1007/s11253-020-01858-y

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