Abstract
The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations.
| Original language | English |
|---|---|
| Pages (from-to) | 413-417 |
| Number of pages | 5 |
| Journal | Advances in Atmospheric Sciences |
| Volume | 18 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2001 |
Funding
In medium-and long-range numerical weather prediction, the finite-difference schemes are extensively employed to carry out the numerical solutions of nonlinear atmospheric equations. So it is a key problem how to design the long-time computational stable difference schemes. Zeng (1978), Zheng and Ji (1981), Wang et al. (1990), Wang and Ji (1994) and Wang et al. (1995) systematically studied the computational stability of the adiabatic or non-dissipative nonlinear evolution equations and constructed the computationally stable implicit and explicit complete square conservative difference schemes. For the forced dissipative nonlinear evolution equations, however, its computational stability analysis has been a little dealt with so far because of its inherent complexity and difficulties. Wang and Ji (1990), Lions et al. (1992), Chou (1995), and Li and Chou (1996, 1997) have systematically carried out the basic theoretical works for the forced dissipative nonlinear evolution equations, analyzed the basic characters of the forced dissipative nonlinear atmospheric systems, transformed the integrated forced dissipative nonlinear atmospheric equations into an equivalent operator equation in Hilbert space and studied the characteristics and physical meanings of the operator. So it provides the theoretical basis for designing computational stable difference schemes. Based on the theoretical basis, Li and Chou (1999) studied the computational stability problem of the forced dissipative nonlinear evolution equations and gave the computational quasi-stability criterion of implicit difference schemes. In this note, the This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCXI-10-07), the National Natural Science Foundation of China (Grant Nos. 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001). Position in the Institute of Physical Ocean, Qingdao Ocean University, Qingdao 266003.
Keywords
- Computational quasi-stability
- Computational stability
- Explicit difference scheme
- Forced dissipative nonlinear evolution equation