З"єднання трансформації Лагерра і швидкої BEM для вирішення початкових граничних задач Діріхле для хвильового рівняння.
We present an improved analysis of two approaches to solving of the Dirichlet initial-boundary value problem for a homogeneous wave equation, which are based on the combination of the Laguerre transform for the time variable with the Galerkin-BEM in an unbounded spatial domain. Both approaches lead to the same in nite triangular system of boundary integral equations as a result. The analysis is done in weighted Sobolev spaces of functions of the time variable taking values in suitable Sobolev spaces. For reducing both storage and computational costs we implement the fast BEM using adaptive cross approximation of obtained matrices. Furthermore, we extend this method for solving the Dirichlet problem in the domain with an inclusion. We also present numerical results for some model problems which illustrate the accuracy and estimated convergence order of the proposed method.
