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We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same...
A two-sided inverse of the differential operator for the unbounded system of elliptic equations on Lipshitz domains was obtained. It was based on a special convolution of sequences. The Dirichlet and Neumann problems for the unbounded systems were reduced to the systems of Fredholm integral equations of either the first kind or the second kind. All equations in integral systems distinguish only by...
A system with infinite quantity of the boundary integral equations which is equivalent to the Dirichlet problem for some triangular system of elliptical equations and its weak formulation has been considered. A recurrent algorithm for solving such systems has been constructed. It involves finding the components of the solution using the boundary elements method step-by-step. The convergence orders...
The Laguerre transform with respect to the time variable has been applied to the Dirichlet problem for the wave equation. Received system of elliptic boundary value problems has been numerically solved with the boundary elements method. Transformants of the time-dependent solution have been represented in form of a simple layer potentials, which densities are determined recurrently from a boundary...
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