Abstract
In the present study, the inverse problem for a multidimensional elliptic equation with mixed boundary conditions and overdetermination is considered. The first and second orders of accuracy in t and the second order of accuracy in space variables for the approximate solution of this inverse problem are constructed. Stability, almost coercive stability, and coercive stability estimates for the solution of these difference schemes are established. For the two-dimensional inverse problems with mixed boundary value conditions, numerical results are presented in test examples.
Highlights
In Section, we present numerical results for a two-dimensional elliptic equation
Τ for uh(λ, x) = ξ h(x), we construct the second order of accuracy difference scheme for inverse problem ( . ), ( . ), ( . )
The second order of accuracy difference scheme is more accurate comparing with the first order of accuracy difference scheme
Summary
Inverse problems for partial differential equations are frequently encountered in various branches of science (see [ – ] and the bibliography therein). Stability and coercive stability estimates for the solution of the first and second order difference schemes for inverse problem ). Our aim in this work is to construct the first and second orders of accuracy difference schemes for an approximate solution of inverse problem In Section , we give theorems on well-posedness of inverse problems with mixed boundary conditions and overdetermination. Section is devoted to the construction of the first and second order difference schemes for approximate solution of problem Λ –l uh(lτ + τ , x) – uh(lτ , x) + o τ τ for uh(λ, x) = ξ h(x), we construct the second order of accuracy difference scheme for inverse problem The difference schemes for nonlocal boundary value problems for the multidimensional elliptic equation were studied in [ , ].
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