半线性奇摄动边值问题的多区域有限差分法数值解

Proceedings. International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Pub Date : 2009-09-26 DOI:10.1109/SYNASC.2009.35

D. Edwards

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引用次数: 0

摘要

描述了一种多区域有限差分方法，并将其应用于一维半线性奇摄动边值问题。本文描述了求解该问题的高精度算法的开发过程，结果表明，当多区域法与这些高阶算法相结合时，数值解的精度可以达到10-20。这比目前的技术提高了9到14个数量级。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Numerical Solution of the Semi Linear Singularly Perturbed Boundary Value Problem Using Multi Region Finite Difference Method

A multi region finite difference method is described and applied to the one dimension, semi linear, singularly perturbed boundary value problem (SPBVP). The process of developing high precision algorithms for this problem is described and it is shown that when the multi region method is combined with the use of these high order algorithms, numerical solutions can achieve accuracies in the range of 10-20. This represents a gain of between 9 to 14 orders of magnitude over current techniques.

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Proceedings. International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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