Nazarov, S. A.; Specovius-Neugebauer, M. Artificial boundary conditions for external boundary problem with a cylindrical inhomogeneity. (Russian, English) Zbl 1114.35016 Zh. Vychisl. Mat. Mat. Fiz. 44, No. 12, 2194-2211 (2004); translation in Comput. Math. Math. Phys. 44, No. 12, 2087-2103 (2004). Local artificial boundary conditions are constructed in exterior Dirichlet and Neumann boundary value problems for a fairly general formally self-adjoint system of second-order differential equations with piecewise constant coefficients. The coefficients have jumps at an infinite cylindrical sur- face with an arbitrary smooth cross section, and the shape of a truncation surface – the boundary of a circular cylinder with a height and diameter of \(2R\) – is adapted to such inhomogeneity. The artificial boundary conditions are constructed without using explicit formulas for the fundamental matrix. Exist- ence and uniqueness theorems are proved for the original and approximating problems, and an asymp- totically sharp error estimate is derived. Reviewer: Andrei Zemskov (Moskva) MSC: 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35J15 Second-order elliptic equations 35G15 Boundary value problems for linear higher-order PDEs Keywords:external boundary problem of Dirichlet and of Neumann; artificial boundary conditions; cylindrical inhomogeneity PDFBibTeX XMLCite \textit{S. A. Nazarov} and \textit{M. Specovius-Neugebauer}, Zh. Vychisl. Mat. Mat. Fiz. 44, No. 12, 2194--2211 (2004; Zbl 1114.35016); translation in Comput. Math. Math. Phys. 44, No. 12, 2087--2103 (2004)