Mathematical Tables and Other Aids to Computation.
Mathematical Tables and Other Aids to Computation.
复制标题
数学表格和其他计算辅助工具。
DOI：
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发表时间：
1946
期刊：
影响因子：
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通讯作者：
D. H. Lehmer
中科院分区：
文献类型：
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作者：
Clare Archibald;D. H. Lehmer
其中y(X)表示该微分方程解。其思想是使用求积公式来估计(1)的积分。这需要了解(xo，-to+h)中指定自变量x的被积函数，因此我们需要这些自变量的y(X)的值。可以使用数值积分方法来估计所需自变量的y(X)。这样，将数值积分方法与求积公式相结合，得到另一种数值积分方法。根据所使用的求积公式和积分方法的组合，可以设计出大量的方法。特别是，高斯两点求积公式与龙格-库塔四阶方法相结合，给出了很好的结果[1]。本文将Radau三点求积公式与Runge-Kutta四阶方法相结合。由此得到的方法似乎在相同工作量的情况下提供了更高的精度。2.方法。Radau求积公式[2]给出了
where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integration method is combined with a quadrature formula to obtain another numerical integration method. A large number of methods may be devised, depending on which combination of quadrature formula and integration method is used. In particular, the Gauss two-point quadrature formula combined with the Runge-Kutta fourth order method appears to give excellent results [1]. We propose here the combination of the Radau three-point quadrature formula with the Runge-Kutta fourth order method. The resulting method seems to give greater accuracy with the same amount of work. 2. The Method. The Radau quadrature formula [2] gives