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Volume 28, Issue 4
Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space

Xiangtuan Xiong & Jinmei Li

DOI: 10.4208/jpde.v28.n4.3

J. Part. Diff. Eq., 28 (2015), pp. 315-331.

Published online: 2015-12

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  • Abstract
In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.
  • Keywords

2D inverse heat conduction problem Ill-posedness regularization error estimate finite difference

  • AMS Subject Headings

65R35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiongxt@gmail.com (Xiangtuan Xiong)

992461300@qq.com (Jinmei Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-315, author = {Xiong , Xiangtuan and Li , Jinmei}, title = {Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {4}, pages = {315--331}, abstract = { In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n4.3}, url = {http://global-sci.org/intro/article_detail/jpde/5119.html} }
TY - JOUR T1 - Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space AU - Xiong , Xiangtuan AU - Li , Jinmei JO - Journal of Partial Differential Equations VL - 4 SP - 315 EP - 331 PY - 2015 DA - 2015/12 SN - 28 DO - http://doi.org/10.4208/jpde.v28.n4.3 UR - https://global-sci.org/intro/article_detail/jpde/5119.html KW - 2D inverse heat conduction problem KW - Ill-posedness KW - regularization KW - error estimate KW - finite difference AB - In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.
Xiong , Xiangtuan and Li , Jinmei. (2015). Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space. Journal of Partial Differential Equations. 28 (4). 315-331. doi:10.4208/jpde.v28.n4.3
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