SPECTRAL COLLOCATION METHODS FOR A PARTIAL INTEGRODIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL

We propose and analyze the spectral collocation approximation for the partial integrodifferential equations with a weakly singular kernel. T he space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We pro ve unconditional stability and obtain the optimal error bounds which d epend on the time step, the degree of polynomial and the Sobolev regul arity of the solution.