Fractional multistep methods were introduced by C. Lubich for the quadrature of Abel integral operators and the solution of weakly singular Volterra integral equations of the first kind with exactly given right-hand sides. In the current paper, we consider the regularizing properties of these methods to solve the mentioned integral equations of the first kind for perturbed right-hand sides. Finally, numerical results are presented.
An initial-value problem for a Fokker-Planck type equation on an unbounded space
domain is discretized in time by an implicit Euler scheme and in space by a Galerkin
scheme. It is shown that this scheme conserves mass, positivity and decay of the
entropy. The approximation properties are investigated and numerical experiments
are provided.