On the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel II: nonsmooth initial data

摘要

Two fractional backward Euler time discretization methods are considered for a linear homogeneous parabolic integrodifferential equation. The first method comes from Part I and the second is based on an equivalent Abel-Volterra type integral equation where the singularity of the exact solution is divided out. Error estimates are derived for these time discretizations. Special attention is paid the case of nonsmooth data.