Abstract
Recently, Goldberg studied in [M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 478-493, M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 1995-2003] stability conditions of a well-known family of difference schemes for the following multidimensional parabolic system of second order:
∂u(x, t)/∂t = ∑1≤p≤q≤s Apq ∂2u(x, t)/∂xp∂xq + ∑1≤p≤s Bp ∂u(x, t)/∂xp + Cu(x, t).
Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.
∂u(x, t)/∂t = ∑1≤p≤q≤s Apq ∂2u(x, t)/∂xp∂xq + ∑1≤p≤s Bp ∂u(x, t)/∂xp + Cu(x, t).
Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.
| Original language | English |
|---|---|
| Pages (from-to) | 548-555 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 38 |
| Issue number | 2 |
| Online published | 19 Jul 2000 |
| DOIs | |
| Publication status | Published - 2000 |
Research Keywords
- Difference schemes
- Parabolic systems
- Stability
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2000 Society for Industrial and Applied Mathematics.