Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain - Berezovsky, A. A.; Mitropolskiy, Yu. A.; Shkhanukov-Lafishev, M. Kh. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We establish the convergence of the Rothe method for a parabolic equation with nonlocal boundary conditions and obtain an a priori estimate for the constructed difference scheme in the grid norm on a ball. We prove that the suggested iterative process for the solution of the posed problem converges in the small.