Displaying similar documents to “On the necessary and sufficient conditions for the convergence of the difference schemes for the general boundary value problem for the linear systems of ordinary differential equations”

Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem

Florian Mehats (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the...

Transfer of boundary conditions for difference equations

Emil Vitásek (2000)

Applications of Mathematics

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It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems. ...