The numerical solution of an evolution problem of second order in time on a closed smooth boundary
This technical paper deals with evolutionary problems having second-order time derivatives and an integral operator coefficient on a closed smooth boundary in \(\mathbb{R}^2\). Combining a Laguerre transformation with a boundary integral method the solution is first developed into a Fourier-Laguerre series. The Laguerre transformation with respect to time leads to an infinite set of operator equations on the boundary. Using single and double layer potentials the solution of the Dirichlet boundary value problem is transformed into boundary integral equations of the second kind with singular kernels. Subsequently, a fully discretzized problem is obtained with Nyström's method using quadrature rules based on trigonometric interpolation. Numerical results illustrate the properties of the method.
scientific article; zbMATH DE number 1787704