A Time–Space Numerical Procedure for Solving the Sideways Heat Conduction Problem

Ching-Chuan Tan, Chao-Feng Shih, Jian-Hung Shen and Yung-Wei Chen ()
Additional contact information
Ching-Chuan Tan: Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
Chao-Feng Shih: Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
Jian-Hung Shen: Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan
Yung-Wei Chen: Department of Marine Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan

Mathematics, 2025, vol. 13, issue 5, 1-17

Abstract: This paper proposes a solution to the sideways heat conduction problem (SHCP) based on the time and space integration direction. Conventional inverse problems depend highly on the available data, particularly when the observed data are contaminated with measurement noise. These perturbations may lead to significant oscillations in the solution. The uniqueness of the solution in this SHCP requires revaluation when boundary conditions (BCs) or initial conditions (ICs) are missing. First, the spatial gradient between two points resolves the missing BCs in the computational domain by a one-step Lie group scheme. Further, the SHCP can be transformed into a backward-in-time heat conduction problem (BHCP). The second-order backward explicit integration can be applied to determine the ICs using the two-point solution at each time step. The performance of the suggested strategy is demonstrated with three numerical examples. The exact solution and the numerical results correspond well, despite the absence of some boundary and initial conditions. The only method of preventing numerical instability in this study is to alter the direction of numerical integration instead of relying on regularization techniques. Therefore, a numerical formula with two integration directions proves to be more accurate and stable compared to existing methods for the SHCP.

Keywords: sideways heat conduction problem (SHCP); backward heat conduction problem (BHCP); Lie group shooting method (LGSM) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/751/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/751/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:751-:d:1599486

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().