On fourth order accuracy stable difference scheme for a multi-point overdetermined elliptic problem

In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multi-point overdetermined boundary value problem for multidimensional elliptic partial differential equations.

A note on well-posedness of source identification elliptic problem in a Banach space

We study the source identification problem for an elliptic differential equation in a Banach space. The exact estimates for the solution of source identification problem in H¨older norms are obtained. In applications, four elliptic source identification problems are investigated. Stability and coercive stability estimates for solution of source identification problems for elliptic equations are obtained.

Numerical solution of a source identification problem: Almost coercivity

The present paper is devoted to the investigation of a source identification problem that describes the flow in capillaries in the case when an unknown pressure acts on the system. First and second order of accuracy difference schemes are presented for the numerical solution of this problem. Almost coercive stability estimates for these difference schemes are established. Additionally, some numerical results are provided by testing the proposed methods on an example.

Well-posedness of a nonlocal boundary value difference elliptic problem

The second order of approximation two-step difference scheme for the numerical solution of a nonlocal boundary value problem for the elliptic differential equation [see formula in PDF] in an arbitrary Banach space E with the positive operator A is presented. The well-posedness of the difference scheme in Banach spaces is established. In applications, the stability, almost coercive stability and coercive stability estimates in maximum norm in one variable for the solutions of difference schemes for numerical solution of two type elliptic problems are obtained.

Well-posedness of boundary value problems for reverse parabolic equation with integral condition

Reverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.

Russian region's coercive stability faces new threats

Subject Violent and peaceful opposition in Chechnya. Significance Multiple attacks on Chechen security forces on August 20 represent a new kind of security risk, different from the activities of conventional armed militants. Claimed by the Islamic State (IS) group, the attacks take place in an broader environment of more vocal criticism of President Ramzan Kadyrov. Impacts Popular discontent will convince Kadyrov to narrow appointments to family and clan. Kadyrov has alienated other North Caucasus leaders and cannot count on their support. The dynamics of IS and other militant activity are likely to remain compartmentalised in each North Caucasus republic.

A fourth order approximation of the Neumann type overdetermined elliptic problem

In this paper, we consider an inverse elliptic problem with Neumann type overdetermination and construct a fourth order of accuracy difference scheme for its solution. Stability, almost coercive stability and coercive stability estimates for the solution of difference problem are proved. Later, we construct a fourth order difference scheme for an inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition. Finally, we illustrate numerical example with descriptions of numeric realization in a two-dimensional case.

High order approximation of the inverse elliptic problem with Dirichlet-Neumann conditions

Inverse problem for the multidimensional elliptic equation with Dirichlet-Neumann conditions is considered. High order of accuracy difference schemes for the solution of inverse problem are presented. Stability, almost coercive stability and coercive stability estimates of the third and fourth orders of accuracy difference schemes for this problem are obtained. Numerical results in a two dimensional case are given.

Approximate Solution of Inverse Problem for Elliptic Equation with Overdetermination

A finite difference method for the approximate solution of the inverse problem for the multidimensional elliptic equation with overdetermination is applied. Stability and coercive stability estimates of the fi rst and second orders of accuracy difference schemes for this problem are established. The algorithm for approximate solution is tested in a two-dimensional inverse problem.