ROMAN CHAPKO AND RAINER KRESS
Rothe's method for parabolic initial boundary value problems, also known as the horizontal line method, consists of a time discretization by finite differences and leads to a sequence of boundary value problems for an inhomogeneous elliptic equation. Whereas in the traditional approach in the solution of this sequence of boundary value problems volume potentials are incorporated, in order to preserve the advantages of the boundary integral equation method we present an approach involving only boundary integrals.