Information on the thesis

For generalized solutions of initial-boundary value problems with Dirichlet
and Neumann conditions for the wave equation with homogeneous initial con-
ditions expansion is constructed in form of Fourier—Laguerre series. These
are obtained from single and double layer retarded potentials by applica-
tion of Laguerre transform. Requirements on function in boundary condition
are obtained that guarantee convergence of solutions in appropriate weighed
Sobolev spaces. Coefficients of expansions are calculated based on solutions
of sequence of boundary integral equations that are solved using boundary
elements method (BEM). Asymptotic error estimates of numerical solutions
are established. Fast BEM, based on adaptive cross approximation of alge-20
braic system is derived. Results of number of numerical experiments confirm
validity of theoretical research and shows effectiveness of developed methods.
Key words: initial-boundary value problems for wave equation, retarded
potentials, Laguerre transform, boundary integral equations, fast boundary
elements method, adaptive cross approximation.