Abstract
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.
Highlights
It is well known that inverse problems arise in various branches of science
We will give the following results of numerical experiments of the inverse problem for the two-dimensional elliptic equation with Dirichlet-Neumann boundary conditions
We present second order of accuracy in t and x difference schemes for problems (35) and (36)
Summary
It is well known that inverse problems arise in various branches of science (see [1, 2]). The theory and applications of well-posedness of inverse problems for partial differential equations have been studied extensively by many researchers (see, e.g., [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and the references therein). Well-posedness of the nonlocal boundary value problems of elliptic type equations was investigated in [18,19,20,21,22,23,24,25] (see the references therein). In [11], the authors established stability estimates for this problem and studied inverse problem for multidimensional elliptic equation with overdetermination in which the Dirichlet condition is required on the boundary
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