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热传导方程反问题的数值解法 被引量:1

Numerical Methods for Solving a Backward Heat Conduction Problem
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摘要 文章分别应用拟边界法和积分方程方法对一类热传导反问题进行了研究,并通过数值算例验证了方法的有效性. In this paper, a backward heat conduction problem is analyzed by quasi-boundary reversibility method and the method of integral equation, and the numerical results show that the methods are effective.
作者 任常青
出处 《四川理工学院学报(自然科学版)》 CAS 2008年第3期28-30,共3页 Journal of Sichuan University of Science & Engineering(Natural Science Edition)
关键词 拟边界法 正则化 反问题 热传导方程 积分方程方法 quasi-boundary method regularization inverse problem backward heat conduction the method of integralequations
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参考文献4

  • 1R Lattes J, Lions L. the Method of Quasi-Reversibility[J]. In: Applications to Partial Differential Equations. New York: American Elseiver, 1969.
  • 2Miller K. Stabilized quasi-reversibility and other nearly best possible methods for non-well-posed problems[A].in: Symposium on Non-Well-Posed Problems and Logarithmic Convexity, Lecture Notes in Mathematics,1973,316: 161-176.
  • 3Gordon W Clark, Seth F. Oppenheimer, Quasi-reversibility, Methods for Non-Well-Posed Problems[J]. Electronic Journal of Differential Equations, 1994, 8: 1-9.
  • 4葛美宝,徐定华,王泽文,张文.一类抛物型方程反问题的数值解法[J].东华理工学院学报,2006,29(3):283-288. 被引量:7

二级参考文献4

  • 1[13]Wei T,Hon Y C.2002.A Meshless Computational Method for Solving Inverse Heat Conduction Problem[J],International Series on Advances in Boundary Elements,13:135-144.
  • 2[10]Elden L.1982.Time discretization in the backward solution of parabolic equation[J].I,Math.Comp.39:53-68.
  • 3[11]Alemdar Hasanov,Jennifer L.Mueller.2001.Anumerical method for backward parabolic with non-selfadjoint elliptic operators[J].Elsevier.Applied Numerical Mathematics,37:55-58.
  • 4[12]Denisov A M.1999.Element of the theory of inverse problem[M].Utrecht:VSP BV

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