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一种求解修正的Helmholtz方程Cauchy问题的数值方法
  • ISSN号：0255-7797
  • 期刊名称：《数学杂志》
  • 时间：0
  • 分类：O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]乌鲁木齐职业大学基础部, [2]兰州大学数学与统计学院
  • 相关基金：国家自然科学基金资助（10671085）
作者： 孙萍[1], 冯晓莉[2]
关键词： 修正的Helmholtz方程, Cauchy问题, 不适定问题, 正则化, 误差估计, modified Helmholtz equation, Cauchy problem, ill-posed problem, regularization, error estimate
中文摘要：

本文研究了无界带形区域Ω={（x,y）｜0〈z〈1，y∈R）上修正的Helmholtz方程的Cauchy问题．利用了一种简便的求解方法获得了Holder型的误差估计．这种方法可以借助于快速Fourier变换和逆变换实现．数值例子说明这种方法非常有效．

英文摘要：

The Cauchy problem for the modified Helmholtz equation in an infinite strip Ω = {（x,y）｜ 0 x 1,y ∈ R} is considered. By using a very simple method for solving the problem, a Hlder type error estimate between the exact solution and it regularization approximation is obtained. Our method can be numerically implemented by fast Fourier transform and inverse fast Fourier transform. Numerical examples show the method works effectively.

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期刊信息
  • 《数学杂志》
  • 北大核心期刊（2011版）
  • 主管单位:中华人民共和国教育部
  • 主办单位:武汉大学 湖北省数学学会 武汉数学学会
  • 主编：陈化
  • 地址：湖北武汉大学
  • 邮编：430072
  • 邮箱：jmath@whu.edu.cn
  • 电话：027-68754687
  • 国际标准刊号：ISSN：0255-7797
  • 国内统一刊号：ISSN：42-1163/O1
  • 邮发代号:38-71
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3910