Uniform l1 Behavior for Time Discretization of a Volterra Equation with Completely Monotonic Kernel II: Convergence
Uniform l1 Behavior for Time Discretization of a Volterra Equation with Completely Monotonic Kernel II: Convergence
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DOI：
10.1137/060668699
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发表时间：
2007-12
期刊：
影响因子：
--
通讯作者：
Xu Da
中科院分区：
文献类型：
--
作者：
Xu Da
推广了前人关于具有完全单调卷积核的Volterra方程解的时间离散化问题。所考虑的时间离散化方法来自第一部分[X]。Da, IMA J. number。分析的。， 22 (2002), pp. 133-151]，其中向后欧拉与近似积分的一阶卷积正交相结合。本文在$l_{t}^{1}(0,\infty;H)\bigcap l_{t}^{\infty}(0,\infty;H)$范数中给出了离散化在时间上的收敛性。
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.