On the Numerical Solution of the Hyperbolic Evolution Problem on Closed Curve

Abstract

AbstractWe consider on evolution problem for a hyperbolic equation with the Dirichlet to Neumann operator. For the numerical solution we combine the Laguerre transformation with respect to the time variable and the boundary integral equation method. Then an infinite sequence of the integral equations of the second kind with a logarithmic singularity is obtained. The full discretization is realized by Nyström's method which is based on trigonometric quadrature rules.