Iterative solution of a nonlinear static beam equation - Berikelashvili , G.; Papukashvili , A.; Peradze, J. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 519.6The paper deals with a boundary-value problem for the nonlinear integro-differential equation $u''''-m \bigg(\int _0^l {u'}^2\,dx \bigg)u'' = f(x, u, u'),$ $m(z)≥ α>0,$ $0≤ z < ∞,$ 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.