Abstract
We study the time discretization for the solution of a Volterra equation with weakly singular kernel. The time discrete scheme is based on the first-order backward difference method. The memory term is approximated by the interpolating quadrature. We use Laplace transform technique to show that this interpolating quadrature scheme has a convergence rate of O(△t) where △t denotes the time step, for smooth and non-smooth initial data in homogeneous case. Special attention is that the uniform l1 convergence property of the discretization in time is given.
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