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首页> 外文会议>International Conference on Computational Science pt.4; 20040606-20040609; Krakow; PL >Application of Extrapolation Methods to Numerical Solution of Fredholm Integral Equations Related to Boundary Value Problems
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Application of Extrapolation Methods to Numerical Solution of Fredholm Integral Equations Related to Boundary Value Problems

机译：外推法在与边值问题有关的Fredholm积分方程的数值解中的应用

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摘要

Fredholm integral equations arise naturally in the context of ordinary and partial differential equations: Two-point boundary value problems can be reformulated as Fredholm integral equations, whose kernels are continuous but have finite jump discontinuities in their derivatives. Two-dimensional elliptic boundary problems can be reformulated as Fredholm integral equations with kernels that have singularities, some having logarithmic singularities. In this note, we describe quadrature methods whose accuracies can be improved at will. These are obtained by improving the underlying numerical quadrature formulas in a clever fashion. In the case of two-point boundary value problems, they are obtained by correcting the trapezoidal rule appropriately to the accuracy required. In the case of boundary integral equations, they are obtained by first correcting the basic trapezoidal rule and then extrapolating it to required accuracy.
机译：Fredholm积分方程在常微分方程和偏微分方程的情况下自然会出现：两点边值问题可以重新定义为Fredholm积分方程，其核是连续的，但其导数具有有限的跳跃间断。二维椭圆边界问题可以重新构造为Fredholm积分方程，其核具有奇异性，有些具有对数奇异性。在本说明中，我们描述了可以任意提高精度的正交方法。这些是通过巧妙地改进基础数字正交公式而获得的。在两点边值问题的情况下，可以通过将梯形规则适当校正到所需的精度来获得它们。对于边界积分方程，可通过首先校正基本梯形规则，然后将其外推至所需的精度来获得。

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