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The outcomes of a search for efficient and correct ways of the truncation of computational domain in finite-difference methods are presented. The relevant mathematical problem is resolved rigorously both for two-dimensional scalar model problems and for three-dimensional vector problems. In the framework of this abstract, we describe briefly only two typical two-dimensional situations. The peculiarities associated with a change to the analysis of three-dimensional vector problems are to be covered in the report.

initial boundary-value problem; absorbing boundary conditions; pulse wave radiation