Abstract
In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.
| Original language | English |
|---|---|
| Pages (from-to) | 59-80 |
| Number of pages | 22 |
| Journal | East Asian Journal on Applied Mathematics |
| Volume | 3 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Feb 2013 |
Scopus Subject Areas
- Applied Mathematics
User-Defined Keywords
- Adams-Bashforth scheme
- Allen-Cahn equation
- Cahn-Hilliard equation
- Crank-Nicolson scheme
- Error estimates
- Implicit-explicit method