Iterative solution of a nonlinear static beam equation - Berikelashvili , G.; Papukashvili , A.; Peradze, J. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 519.6 The paper deals with a boundary-value problem for the nonlinear integro-differential equation u’’’’-m (_0^l u’^2 dx )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.