Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method
We construct a high order finite difference method in which quadrature points do not need to have a lattice structure. In order to develop our method we show two tools using Fourier transform and Taylor expansion, respectively. On the other hand, the backward heat conduction problem is a typical exa...
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| Published in: | Journal of the Chinese Institute of Engineers Vol. 27; no. 4; pp. 611 - 620 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
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Taylor & Francis Group
01.06.2004
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| ISSN: | 0253-3839, 2158-7299 |
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| Abstract | We construct a high order finite difference method in which quadrature points do not need to have a lattice structure. In order to develop our method we show two tools using Fourier transform and Taylor expansion, respectively. On the other hand, the backward heat conduction problem is a typical example of ill-posed problems in the sense that the solution is unstable for errors of data. Our aim is creation of a meshless method which can be applied to the ill-posed problem. From numerical experiments we confirmed that our method is effective in solving two-dimensional backward heat conduction equations subject to the Dirichlet boundary condition. |
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| AbstractList | We construct a high order finite difference method in which quadrature points do not need to have a lattice structure. In order to develop our method we show two tools using Fourier transform and Taylor expansion, respectively. On the other hand, the backward heat conduction problem is a typical example of ill-posed problems in the sense that the solution is unstable for errors of data. Our aim is creation of a meshless method which can be applied to the ill-posed problem. From numerical experiments we confirmed that our method is effective in solving two-dimensional backward heat conduction equations subject to the Dirichlet boundary condition. |
| Author | Iijima, Kentaro |
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| CitedBy_id | crossref_primary_10_1016_j_ijheatmasstransfer_2010_06_050 crossref_primary_10_1016_j_ijheatmasstransfer_2018_10_083 crossref_primary_10_1016_j_matcom_2007_11_005 crossref_primary_10_1108_HFF_04_2012_0083 crossref_primary_10_1016_j_ijheatmasstransfer_2006_10_050 crossref_primary_10_1080_10407790_2011_588134 crossref_primary_10_1016_j_ijthermalsci_2018_01_001 crossref_primary_10_1016_j_ijheatmasstransfer_2022_123627 crossref_primary_10_1016_j_ijheatmasstransfer_2010_12_013 crossref_primary_10_1080_02533839_2009_9671510 crossref_primary_10_1016_j_ijheatmasstransfer_2016_01_008 crossref_primary_10_3390_math12172629 crossref_primary_10_1016_j_enganabound_2010_03_010 crossref_primary_10_1016_j_ijheatmasstransfer_2014_12_057 crossref_primary_10_1155_2013_205169 crossref_primary_10_1016_j_enganabound_2025_106280 crossref_primary_10_1155_2018_1868921 crossref_primary_10_1016_j_ijheatmasstransfer_2010_05_036 crossref_primary_10_1080_10407790_2017_1420317 crossref_primary_10_1016_j_ijheatmasstransfer_2015_09_057 crossref_primary_10_1016_j_apnum_2018_02_002 crossref_primary_10_1016_j_amc_2019_02_035 crossref_primary_10_1016_j_apnum_2010_09_006 crossref_primary_10_1016_j_ijheatmasstransfer_2018_12_103 crossref_primary_10_1016_j_accre_2021_10_003 crossref_primary_10_1080_02533839_2010_9671608 crossref_primary_10_1007_s13160_015_0203_7 |
| Cites_doi | 10.1007/978-3-642-84108-8 10.1007/978-3-642-97146-4 |
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| References | Richtmyer R. D. (CIT0006) 1967 Imai H. (CIT0003) 1999; 9 Kress R. (CIT0005) 1989; 82 Ito S. (CIT0004) 1963 Fujiwara H. (CIT0002) 2001; 50 Canuto C. (CIT0001) 1988 |
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| Title | Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method |
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