Quadrature methods for some boundary integral equations of parabolic type

We consider quadrature methods for the single and the double layer heat equations corresponding to the two dimensional heat conduction problem. We combine the collocation with respect to the time variable and a modified quadrature method with respect to the spatial variable. Ebr this method (called MCQ method) the discretizations, using piecewise constant and piecewise linear splines, are presented. In the last section of this work we report results from some numerical experiments.