Uniform $l^{1}$ Behavior for Time Discretization of a Volterra Equation with Completely Monotonic Kernel II: Convergence

Authors:
Xu Da
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2008

Citing 0
Cited 3

The numerical analysis on a Volterra equation with asymptotically periodic solution

Journal of Computational and Applied Mathematics
Uniform $l^1$ Behavior of a Time Discretization Method for a Volterra Integrodifferential Equation with Convex Kernel; Stability

SIAM Journal on Numerical Analysis
Uniform $$l^{1}$$ behavior in the Crank---Nicolson methods for a linear Volterra equation with convex kernel

Calcolo: a quarterly on numerical analysis and theory of computation

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Abstract

A previous work on the time discretization for the solution of a Volterra equation with completely monotonic convolution kernel is extended. The considered time discretization method comes from Part I [X. Da, IMA J. Numer. Anal., 22 (2002), pp. 133-151], where the backward Euler is combined with order one convolution quadrature approximating the integral. In the present paper, the convergence properties of the discretization in time are given in the $l_{t}^{1}(0,\infty;H)\bigcap l_{t}^{\infty}(0,\infty;H)$ norm.