An approximation method for the hypersingular heat operator equation (Q1971829)

Starting with the 2D equation of heat conductivity with zero initial data and Neumann boundary conditions, the author studies a numerical method for solving the related boundary integral formulation that is a hypersingular integral equation. The method, which can be interpreted as a Petrov-Galerkin scheme, uses tensor products of cubic splines in space and linear splines in time. In opposite to other methods known from the literature, the approximation here relies upon a collocation in space and not upon a boundary element method. Stability analysis and suboptimal convergence is provided for the case the spatial domain is a disk.