Rothe's method for the heat equation and boundary integral equations

Abstract

Rothes 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 inhomo-geneous 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. © 1997 Rocky Mountain Mathematics Consortium.