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逆热传导方程的一个正则化方法 被引量:1

A Regularization for Solving the Sideways Heat Equation
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摘要 考虑了标准的一维逆热传导方程.问题是不适定的,即解不连续地依赖于数据.通过Fourier逼近的方法进行正则化处理,提出了一个新的算法,理论分析和数值实验均表明该算法是稳定的;该算法不仅保留了测量数据的部分高频成份,同时还具有相同的精度和计算复杂性. This paper considers an inverse heat conduction problem, the sideways heat equation. The problem is ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. A new algorithm is proposed to regularize this problem by a Fourierbased approximation. The theory analysis and numerical experiments prove it is stable. 'This algorithm not only keeps parts of high-frequency components of the data, but also presents the same accurate and computing complexity.
出处 《数学的实践与认识》 CSCD 北大核心 2007年第21期44-48,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(10571008)
关键词 逆问题 不适定问题 FOURIER分析 热传导 Inverse problem Ill-posed problem Fourier analysis heat conduction
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参考文献5

  • 1Elden L, Berntsson F, Reginska T. Wavelet and Fourier method for solving the sideways heat equation[J]. SIAM J SCI COMPUT, 2000,21(6): 2187-2205.
  • 2Reginska T, Elden L. Solving the sideways heat equation by a Wavelet-Galerkin method [J]. Inverse Problems, 1997,13(5) : 1093-1106.
  • 3Cannon J R. The One Dimensional Heat Equation[M]. Reading, MA: Addislon-Wesley, 1984.
  • 4Dinh N ho Hao, H-J Reinhardt. On a sideways parabolic equation[J]. Inverse Problems, 1997,13(4):297-309.
  • 5Elden L. Numerical solution of the sideways heat equation by difference approximation in time [J]. Inverse Problem, 1995,11 : 913-923.

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