Time discretization of parabolic boundary integral equations (Q1326416)

A time discretization procedure for time-dependent boundary integral equations which is based on linear multistep methods is proposed. The method works in cases where the Laplace transform of the fundamental solution is explicitly known. If no space discretization is considered the method yields numerical solutions identical to a semi-discretization in time of the partial differential equation by the underlying multistep method. Results concerning stability properties and convergence estimates are obtained and numerical examples are included.