Spline collocation for convolutional parabolic boundary integral equations

Abstract. We consider spline collocation methods for a class of parabolic pseudodiffer-ential operators. We show optimal order convergence results in a large scale of anisotropic Sobolev spaces. The results cover for example the case of the single layer heat operator equation when the spatial domain is a disc. 1. Introduction. The integral equation method for the solution of parabolic problems is known already for a long time, for the early literature see [23],[21],[28,29,30]. The reasons which recom-mend this method instead of the domain methods are similar as in the elliptic case. The main arguments are: In the level of the numerical implementation there is a reductio