A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations

Advances in Atmospheric Sciences

Volumn 19, Issue 4, 2002, Pages 699-704

  Lin, Wantao ^a,b   Ji, Zhongzhen ^a   Wang, Bin ^a  

^a INSTITUTE OF ATMOSPHERIC PHYSICS   (China)

^b OCEAN UNIVERSITY OF CHINA   (China)

Author keywords

Computational stability; Difference scheme; Evolution equation; Initial value

Indexed keywords

EID: 0346044572     PISSN: 02561530     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00376-002-0009-9     Document Type: Article

References (14)

1. Hirt, C. W., 1968: Heuristic stability theory for finite-difference equations. J. Comput. Phys., 2, 339-355.
2. Ji Zhongzhen, 1981a: An example of nonlinear computational instability for two-dimensional "Lilly scheme". Chinese Science Bulletin, 26(2), 153-155.
3. Ji Zhongzhen, 1981b: A comparative analysis for non-linear computational stability. Chinese Journal of Atmospheric Sciences, 4(4), 344-354 (in Chinese).
4. Ji Zhongzhen, and Wang Bin, 1991: Further discussion on the construction and application of difference schemes of evolution equations. Chinese Journal of Atmospheric Sciences, 15(2), 72-78 (in Chinese).
5. Ji Zhongzhen, Wang Bin, and Zeng Qingcun, 1998: Some new advances in computational geophysical fluid dynamics. Acta Aerodynamica Sinica, 16(1), 108-114 (in Chinese).
6. Lin Wantao, Ji Zhongzhen, Wang Bin, and Yang Xiaozhong, 2000: A new method for judging the computational stability of the difference schemes of non-linear evolution equations. Chinese Science Bulletin, 45(15), 1358-1361.
7. Von Neumann, J., and R. D. Richtmyer, 1950: A method for the numerical calculation of hydrodynamical shocks. J. Appl. Phys., 21, 232-257.
8. Wang Bin, and Ji Zhongzhen, 1990: The construction and preliminary test of the complete square conservative difference schemes. Chinese Science Bulletin, 35(20), 1724-1728.
9. Wang Bin, and Ji Zhongzhen, 1994: The harmonious dissipative operators and the completely square conservative difference schemes in an explicit way. Science in China (Series B), 37(4), 462-471.
10. Wang Bin, Zeng Qingcun, and Ji Zhongzhen, 1995: Square conservation systems and Hamiltonian systems. Science in China (Series A), 38(10), 1211-1219.
11. Warming R. F., and B. J. Hyett, 1974: The modified equation approach to the stability and accuracy analysis of finite-difference methods. J. Comput. Phys., 14, 159-179.
12. Wu Jianghang, and Han Qingshu, 1988: The Theory, Method and Application of Computational Fluid Dynamics. Science Press, Beijing, 293pp (in Chinese).
13. Zeng Qingcun, 1978: Some problems of computational stability. Chinese Journal of Atmospheric Sciences, 2(3), 181-191 (in Chinese).
14. Zeng Qingcun, and Ji Zhongzhen, 1981: On the computational stability of evolution equations. Chinese Journal of Computational Mathematics, 3(1), 79-86 (in Chinese).