CONVOLUTION QUADRATURE AND DISCRETIZED OPERATIONAL CALCULUS .1.
CONVOLUTION QUADRATURE AND DISCRETIZED OPERATIONAL CALCULUS .1.
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DOI：
10.1007/bf01398686
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发表时间：
1988-01-01
影响因子：
2.1
通讯作者：
LUBICH, C
中科院分区：
文献类型：
--
作者：
LUBICH, C
推导了积分方程（Volterra， Wiener-Hopf方程）和数值积分（奇异积分，多时间尺度卷积）问题的数值方法。这个理论的基本工具是用卷积积分规则对卷积积分进行数值逼近。这里，* g (x)在网格上的近似值=0,h, 2h，…， NhtN是在同一网格上与g值进行离散卷积得到的。利用拉普拉斯变换和线性多步法确定正交权值。证明了卷积求积法收敛于基础多步法的阶数。
Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integralsby convolution quadrature rules. Here approximations tof* g (x) on the gridx=0,h, 2h, ..., NhtN hare obtained from a discrete convolution with the values of g on the same grid. The quadrature weights are determined with the help of the Laplace transform offand a linear multistep method. It is proved that the convolution quadrature method is convergent of the order of the underlying multistep method.