Nyström discretization of parabolic boundary integral equations
A Nystrom method for the discretization of thermal layer potentials is proposed and analyzed. The method is based on considering the potentials as generalised Abel integral operators in time, where the kernel is a time dependent surface integral operator. The time discretization is the trapezoidal rule with a corrected weight at the end point to compensate for singularities of the integrand. The spatial discretization is a standard quadrature rule for surface integral of smooth functions. The explicit method developed by this discretization is used to solve the Neumann problem for the heat equation in the exterior of the unit sphere. The numerical results are in good agreement with the theoretical estimates.
scientific article; zbMATH DE number 5608062
scientific article