Iterative solution of a nonlinear static beam equation

  • G. Berikelashvili Georg. Techn. Univ., Tbilisi; A. Razmadze Math. Inst., Tbilisi, Georgia
  • A. Papukashvili I. Javakhishvili Tbilisi State Univ.; I. Vekua Inst. Appl. Math., Tbilisi, Georgia
  • J. Peradze Georg. Techn. Univ., Tbilisi; I. Javakhishvili Tbilisi State Univ., Georgia

Abstract

UDC 519.6

The paper deals with a boundary-value problem for the nonlinear integro-differential equation $u''''-m \bigg(\int _0^l {u'}^2\,dx \bigg)u''  = f(x, u, u'),$ $m(z)\geq \alpha>0,$ $0\leq z < \infty,$ modeling the static state of the Kirchhoff beam.  The problem is reduced to a nonlinear integral equation, which is solved using the Picard iteration method.  The convergence of the iteration process is established and the error estimate is obtained.

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Published
18.08.2020
How to Cite
Berikelashvili G., Papukashvili A., and PeradzeJ. “Iterative Solution of a Nonlinear Static Beam Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 8, Aug. 2020, pp. 1024-33, doi:10.37863/umzh.v72i8.833.
Section
Research articles