MINRES法和有限元法解奇摄动反应扩散方程 |
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作者姓名: | 尹军伟 陈玉福 |
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作者单位: | 中国科学院研究生院数学科学学院, 北京 100049 |
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摘 要: | 讨论奇摄动反应扩散方程 的数值逼近求解问题, 及 均为正实数. 利用有限元方法并结合最小残量法, 给出求解该问题的一个新方 法, 该方法修正了单纯采用有限元方法求解时在边界附近呈现出的非正常扰动的 现象, 避免了因为 过小所引起的解的变异, 从而得到更加精确的数值结果.
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关 键 词: | 最小残量法 有限元方法 奇摄动反应扩散方程 |
MINRES and finite element method for singularly perturbed reaction diffusion equations |
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Authors: | YIN Jun-Wei CHEN Yu-Fu |
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Institution: | School Of Mathematical Sciences, Graduate University of the Chinese Academy Of ;Sciences, Beijing 100049, China |
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Abstract: | In this paper, we discuss the numerical solutions of singularly perturbed reaction diffusion equation , where both and are positive constants. Based on the finite element method, we use the MINRES algorithm to obtain numerical solutions of the equation. Our new approach corrects the spurious oscillations in the presence of boundary layers of the original solutions. |
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Keywords: | MINRES algorithm finite element method singularly perturbed reaction diffusion equation |
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