In the paper the convergence of a finite difference scheme for two-dimensional nonlinear elliptic equation in the rectangular domain with the integral boundary condition is considered. The majorant is constructed for the error of the solution of the system of difference equations, and the estimation of this error is obtained. With this aim, the idea of application of the M-matrices for the theoretical...
We deal with the stability of a locally one-dimensional method for two-dimensional parabolic equations subject to nonlocal boundary condition. To analyze the stability, we study the structure of the spectrum of the transition matrix of the difference scheme. The results of a numerical experiment are presented.
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