document: The numerical solution of an evolution problem of second order in time on a closed smooth boundary 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
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