Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem
In this paper we consider a numerical method for solving nonhomogeneous backward heat conduction problem. Coupled with the likewise Crank Nicolson scheme and an intermediate variable, the backward problem is transformed to a nonhomogeneous Helmholtz type problem; the unknown initial temperature can...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2018/1868921 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553057786789888 |
|---|---|
| author | LingDe Su TongSong Jiang |
| author_facet | LingDe Su TongSong Jiang |
| author_sort | LingDe Su |
| collection | DOAJ |
| description | In this paper we consider a numerical method for solving nonhomogeneous backward heat conduction problem. Coupled with the likewise Crank Nicolson scheme and an intermediate variable, the backward problem is transformed to a nonhomogeneous Helmholtz type problem; the unknown initial temperature can be obtained by solving this Helmholtz type problem. To illustrate the effectiveness and accuracy of the proposed method, we solve several problems in both two and three dimensions. The results show that this numerical method can solve nonhomogeneous backward heat conduction problem effectively and precisely, even though the final temperature is disturbed by significant noise. |
| format | Article |
| id | doaj-art-516b38d9b8c44a479a71501f64e3bd3f |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-516b38d9b8c44a479a71501f64e3bd3f2025-02-03T05:57:07ZengWileyInternational Journal of Differential Equations1687-96431687-96512018-01-01201810.1155/2018/18689211868921Numerical Method for Solving Nonhomogeneous Backward Heat Conduction ProblemLingDe Su0TongSong Jiang1Institute of Mathematics and Information Science, North-Eastern Federal University, RussiaDepartment of Mathematics, Heze University, Shandong, ChinaIn this paper we consider a numerical method for solving nonhomogeneous backward heat conduction problem. Coupled with the likewise Crank Nicolson scheme and an intermediate variable, the backward problem is transformed to a nonhomogeneous Helmholtz type problem; the unknown initial temperature can be obtained by solving this Helmholtz type problem. To illustrate the effectiveness and accuracy of the proposed method, we solve several problems in both two and three dimensions. The results show that this numerical method can solve nonhomogeneous backward heat conduction problem effectively and precisely, even though the final temperature is disturbed by significant noise.http://dx.doi.org/10.1155/2018/1868921 |
| spellingShingle | LingDe Su TongSong Jiang Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem International Journal of Differential Equations |
| title | Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem |
| title_full | Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem |
| title_fullStr | Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem |
| title_full_unstemmed | Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem |
| title_short | Numerical Method for Solving Nonhomogeneous Backward Heat Conduction Problem |
| title_sort | numerical method for solving nonhomogeneous backward heat conduction problem |
| url | http://dx.doi.org/10.1155/2018/1868921 |
| work_keys_str_mv | AT lingdesu numericalmethodforsolvingnonhomogeneousbackwardheatconductionproblem AT tongsongjiang numericalmethodforsolvingnonhomogeneousbackwardheatconductionproblem |