Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation
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| Title: | Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation |
|---|---|
| Authors: | Castro, María Ángeles | Martín Alustiza, José Antonio | Rodríguez, Francisco |
| Research Group/s: | Análisis de Datos y Modelización de Procesos en Biología y Geociencias |
| Center, Department or Service: | Universidad de Alicante. Departamento de Matemática Aplicada |
| Keywords: | Unconditional stability | Numerical method | Dual-phase-lag equation |
| Knowledge Area: | Matemática Aplicada |
| Issue Date: | 30-Mar-2017 |
| Publisher: | Hindawi Publishing Corporation |
| Citation: | M. A. Castro, J. A. Martín, and F. Rodríguez, “Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation,” Mathematical Problems in Engineering, vol. 2017, Article ID 1650380, 5 pages, 2017. doi:10.1155/2017/1650380 |
| Abstract: | The stability properties of a numerical method for the dual-phase-lag (DPL) equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established. |
| Sponsor: | This work was partially funded by Grant GRE12-08 from University of Alicante. |
| URI: | http://hdl.handle.net/10045/65068 |
| ISSN: | 1024-123X (Print) | 1563-5147 (Online) |
| DOI: | 10.1155/2017/1650380 |
| Language: | eng |
| Type: | info:eu-repo/semantics/article |
| Rights: | © 2017 M. A. Castro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Peer Review: | si |
| Publisher version: | http://dx.doi.org/10.1155/2017/1650380 |
| Appears in Collections: | INV - MODDE - Artículos de Revistas |
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| File | Description | Size | Format | |
|---|---|---|---|---|
 2017_Castro_etal_MathProblemsEng.pdf | 2,07 MB | Adobe PDF | Open Preview | |
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