On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations
On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations
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DOI：
10.1007/s002110050033
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发表时间：
1994-04
影响因子：
2.1
通讯作者：
C. Lubich
中科院分区：
文献类型：
--
作者：
C. Lubich
Convergence estimates in terms of the data are shown for multistep methods applied to non-homogeneous linear initial-boundary value problems. Similar error bounds are derived for a new class of time-discrete and fully discrete approximation schemes for boundary integral equations of such problems, e.g., for the single-layer potential equation of the wave equation. In both cases, the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions. These estimates, which are also proved here, depend on bounds of the Laplace transform of the (distributional) convolution kernel outside the stability region scaled by the time stepsize, and on the smoothness of the data.
