基于新Marchuk积分恒等式的一维界面问题高阶差分格式

J. Num. Math. Pub Date : 2005-04-01 DOI:10.1515/1569395054068982

I. Angelova, L. Vulkov

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引用次数: 2

摘要

构造并分析了一维模型界面问题解和通量的高阶有限差分近似。基于新的Marchuk积分恒等式，导出了精度为0 (h 2)， 0 (h 4)，…的显式公式。开发了利用Lobatto正交计算任意精度阶的三点格式的数值积分程序。给出了一个严格的收敛速度分析。数值实验证实了理论结果。

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High-order difference schemes based on new Marchuk integral identities for one-dimensional interface problems

High-order finite difference approximations of the solution and the flux to model interface problems in one-dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O(h 2), O(h 4),… accuracy are derived. Numerical integration procedures using Lobatto quadratures for computing three-point schemes of any prescribed order of accuracy are developed. A rigorous rate of convergence analysis is presented. Numerical experiments confirm the theoretical results.

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J. Num. Math.

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