The Linear Barycentric Rational Quadrature Method for Volterra Integral Equations
The Linear Barycentric Rational Quadrature Method for Volterra Integral Equations
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DOI：
10.1137/120904020
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发表时间：
2014-01
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影响因子：
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通讯作者：
Jean-Paul Berrut;S. A. Hosseini;Georges Klein
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文献类型：
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作者：
Jean-Paul Berrut;S. A. Hosseini;Georges Klein
介绍了求解一般第二类Volterra积分方程的两种基于线性有理插值法的直接求积法。第一种是由前人给出的线性重心有理求积的直接应用而得到的，其收敛速度与有理求积规则相同，但在长积分区间上是昂贵的。第二种是基于这种求积规则的复合版本，它失去了一阶收敛，但成本要低得多。这两种方法都只需要在等间距节点处的所涉及的函数的样本，并以机器精度产生大多数经典例子的无限光滑解。
We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate as the rational quadrature rule but is costly on long integration intervals. The second, based on a composite version of this quadrature rule, loses one order of convergence but is much cheaper. Both require only a sample of the involved functions at equispaced nodes and yield an infinitely smooth solution of most classical examples with machine precision.