Finite difference method for Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions

Abstract

In this paper, we apply finite difference method to Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions. Stability, coercive stability inequalities for solution of the first and second order of accuracy difference schemes (ADSs) are proved. Then, established abstract results are applied to get stable difference schemes for Bitsadze-Samarskii type overdetermined elliptic multidimensional differential problems with multipoint nonlocal boundary conditions. Finally, numerical results with explanation on the realization in two dimensional and three dimensional cases are presented.

On the absolute stable difference scheme for the space‐wise dependent source identification problem for elliptic‐telegraph equation

“…Applying formula (16) and estimates (27) and (30) and the triangle inequality, we obtain estimate (25). Second, we obtain the estimate ||Av k || H for −N ≤ k ≤ N. Using formulas (17) and 18and Abel's formula, we can get formulas…”

“…Several local and nonlocal BVPs for elliptic, hyperbolic, telegraph, hyperbolic‐telegraph, and elliptic–hyperbolic differential and difference equations have been investigated by many scientists (see [13–35] and the references given therein).…”