Abstract
We first summarize the general concept of our verification method of solutions for elliptic equations. Next, as an application of our method, a survey and future works on the numerical verification method of solutions for heat convection problems known as Rayleigh-Bénard problem are described. We will give a method to verify the existence of bifurcating solutions of the two-dimensional problem and the bifurcation point itself. Finally, an extension to the three-dimensional case and future works will be described.
| Original language | English |
|---|---|
| Pages (from-to) | 443-463 |
| Number of pages | 21 |
| Journal | Japan Journal of Industrial and Applied Mathematics |
| Volume | 26 |
| Issue number | 2-3 |
| Publication status | Published - 2009 Oct |
| Externally published | Yes |
Fingerprint
Keywords
- Bifurcation point
- Elliptic equations
- Numerical verification method
- Rayleigh-Bénard problem
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
Cite this
Watanabe, Y., & Nakao, M. T. (2009). Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. Japan Journal of Industrial and Applied Mathematics, 26(2-3), 443-463.