Abstract
The overdetermination problem for elliptic differential equation with Dirichlet boundary condition is considered. The third and fourth orders of accuracy stable difference schemes for the solution of this inverse problem are presented. Stability, almost coercive stability, and coercive inequalities for the solutions of difference problems are established. As a result of the application of established abstract theorems, we get well-posedness of high order difference schemes of the inverse problem for a multidimensional elliptic equation. The theoretical statements are supported by a numerical example. MSC:35N25, 39A14, 39A30, 65J22.
Highlights
1 Introduction Many problems in various branches of science lead to inverse problems for partial differential equations [ – ]
In Section, we present the third and fourth order difference schemes for problem ( . ) and obtain stability estimates for them
4 Numerical results by using the third and fourth order of the accuracy approximation, we obtain an approximate solution of the inverse problem u(t,x) ∂t
Summary
Many problems in various branches of science lead to inverse problems for partial differential equations [ – ]. The first and second accuracy stable difference schemes for this problem have been constructed in [ ]. High order of accuracy stable difference schemes for nonlocal boundary value elliptic problems are presented in [ – ]. Our aim in this work is the construction of the third and fourth order stable accuracy difference schemes for the inverse problem
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