TY - JOUR
AU - G. Berikelashvili
AU - A. Papukashvili
AU - J. Peradze
PY - 2020/08/18
Y2 - 2020/09/25
TI - Iterative solution of a nonlinear static beam equation
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 8
SE - Research articles
DO - 10.37863/umzh.v72i8.833
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/833
AB - UDC 519.6The paper deals with a boundary-value problem for the nonlinear integro-differential equation $u''''-m \bigg(\int _0^l {u'}^2\,dx \bigg)u'' = f(x, u, u'),$ $m(z)\geq \alpha>0,$ $0\leq z < \infty,$ 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.
ER -