A QUASI-BOUNDARY VALUE REGULARIZATION METHOD FOR A FRACTIONAL-DIFFUSION INVERSE HEAT CONDUCTION PROBLEM

Zhi-Liang Deng; Xiao-Mei Yang

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A QUASI-BOUNDARY VALUE REGULARIZATION METHOD FOR A FRACTIONAL-DIFFUSION INVERSE HEAT CONDUCTION PROBLEM

机译：分数-扩散逆热传导问题的拟边界值正则化方法

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In this paper, the ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed. A quasi-boundary value regularization method is discussed. An a priori parameter choice rule is discussed and the corresponding error estimate between the exact solution and its regularized approximation is obtained. Moreover, a numerical example is provided to verify our theoretical results.

机译：本文讨论了控制线性扩散方程为分数形式时试图从一个测得的一维半无限导体内点的瞬态数据温度恢复温度函数的不适定问题。讨论了一种准边界值正则化方法。讨论了先验参数选择规则，并获得了精确解与其正则化近似值之间的相应误差估计。此外，提供了一个数值示例来验证我们的理论结果。

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来源
《International journal of numerical methods and applications》 |2011年第2期|p.137-147|共11页
作者
Zhi-Liang Deng; Xiao-Mei Yang;
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作者单位

School of Mathematics Science University of Electronic Science and Technology of China Chengdu 610054, P. R. China;

College of Mathematics Southwest Jiaotong University Chengdu 610031, P. R. China;

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原文格式 PDF
正文语种 eng
中图分类
关键词
fractional-diffusion equation; ill-posed problems; quasi-boundary value method; error estimate; a posteriori;

机译：分数扩散方程不适的问题;准边界值法误差估计;后验;

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2. A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem [J] . Zhi-LiangDeng, Xiao-MeiYang, Xiao-LiFeng Mathematical Problems in Engineering: Theory, Methods and Applications . 2013,第5期

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3. A NEW SHOOTING METHOD FOR QUASI-BOUNDARY REGULARIZATION OF MULTI-DIMENSIONAL BACKWARD HEAT CONDUCTION PROBLEMS [J] . Chang CW, Liu CS, Chang JR Journal of the Chinese Institute of Engineers . 2009,第3期

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4. An Inverse Heat Conduction Problem in Estimating Surface Heat Flux by Bregman Regularization Method [C] . Tao Tan, Xingsi Li 第一届高聚物成型加工与材料物性预测国际学术研讨会论文集 . 2006

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7. A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem [O] . Zhi-Liang Deng, Xiao-Mei Yang, Xiao-Li Feng 2013

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8. Sequential Regularization Solution of the Inverse Heat Conduction Problem [R] . Beck, J. V., Blackwell, B. F., St. Clair, C. R. 1985

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A QUASI-BOUNDARY VALUE REGULARIZATION METHOD FOR A FRACTIONAL-DIFFUSION INVERSE HEAT CONDUCTION PROBLEM

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