title: The numerical solution of an evolution problem of second order in time on a closed smooth boundary
abstract: We consider an initial value problem for the second-order differential equation with a Dirichlet-to-Neumann operator coefficient. For the numerical solution we carry out semi-discretization by the Laguerre transformation with respect to the time variable. Then an infinite system of the stationary operator equations is obtained. By potential theory, the operator equations are reduced to boundary integral equations of the second kind with logarithmic or hypersingular kernels. The full discretization is realized by Nystrom's method which is based on the trigonometric quadrature rules. Numerical tests confirm the ability of the method to solve these types of nonstationary problems
keyphrases: evolution problem closed smooth boundary initial value problem second-order differential equation Laguerre transformation stationary operator equations boundary integral equations hypersingular kernels