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奇异摄动反应扩散问题的高阶不等距计算方法

蔡新 蔡丹琳 吴瑞潜 谢康和

蔡新, 蔡丹琳, 吴瑞潜, 谢康和. 奇异摄动反应扩散问题的高阶不等距计算方法[J]. 应用数学和力学, 2009, 30(2): 171-178.
引用本文: 蔡新, 蔡丹琳, 吴瑞潜, 谢康和. 奇异摄动反应扩散问题的高阶不等距计算方法[J]. 应用数学和力学, 2009, 30(2): 171-178.
CAI Xin, CAI Dan-lin, WU Rui-qian, XIE Kang-he. High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem[J]. Applied Mathematics and Mechanics, 2009, 30(2): 171-178.
Citation: CAI Xin, CAI Dan-lin, WU Rui-qian, XIE Kang-he. High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem[J]. Applied Mathematics and Mechanics, 2009, 30(2): 171-178.

奇异摄动反应扩散问题的高阶不等距计算方法

基金项目: 国家自然科学基金资助项目(50679074);福建省教育厅基金资助项目(JA08140,A0610025);浙江科技学院科研启动基金资助项目(2008050)
详细信息
    作者简介:

    蔡新(1964- ),男,福建泉州人,教授,博士(联系人.Tel/Fax:+86-592-6182935;E-mail:cxxm05@126.com).

  • 中图分类号: O241.81

High Accurate Non-Equidlstant Method for Singular Perturbation Reaction-Diffusion Problem

  • 摘要: 考虑奇异摄动反应扩散方程,这是一个多尺度问题,问题在左右两边皆产生边界层现象.根据边界层的奇性,提出不等距的有限差分格式,其主要思想是根据Shishkin过渡点将区域分为边界层区域和边界层外区域,在边界层外采用等距的大步长,在边界层区域内逐步增加网格步长,有一半的网格步长是不同的.进行了截断误差估计,并证明所提方法是稳定的,一致收敛性高于2阶.最后给出数值例子以说明理论结果的正确性.
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出版历程
  • 收稿日期:  2008-06-25
  • 修回日期:  2008-12-04
  • 刊出日期:  2009-02-15

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