Computational uncertainty principle in nonlinear ordinary differential equations - II. Theoretical analysis

Science in China, Series E: Technological Sciences

Volumn 44, Issue 1, 2001, Pages 55-74

  Li, Jianping ^a   Zeng, Qingcun ^a   Chou, Jifan ^b  

^a INSTITUTE OF ATMOSPHERIC PHYSICS   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Computational uncertainty principle; Convergence; Discretization error; Machine precision; Maximally effective computation time (MECT); Optimal stepsize (OS); Round off error; Universal relation

Indexed keywords

EID: 0035245844     PISSN: 10069321     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02916726     Document Type: Article

References (12)

1. Li Jianping, Zeng Qingcun, Chou Jifan, Computational Uncertainty Principle in Nonlinear Ordinary Differential Equations I. Numerical Results, Science in China, Ser. E, 2000, 43(5): 449
2. Henrici, P., Discrete Variable Methods in Ordinary Differential Equations, New York: John Wiley, 1962, 1; 187.
3. Henrici, P., Error Propagation for Difference Methods, New York: John Whiley, 1963.
4. Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Englewood Cliffs, NJ: Prentice-Hall, 1971, 1; 72.
5. Hairer, E., Nørsett, S. P., Wanner, G., Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd ed., Berlin-Heidelberg-New York: Springer-Verlag, 1993, 130.
6. Stoer, J., Bulirsch, R., Introduction to Numerical Analysis, 2nd ed., Vol. 1, Berlin-Heidelberg-New York: Springer-Verlag (reprinted in China by Beijing Wold Publishing Corporation), 1998, 428.
7. Li Qingyang, Numerical Methods in Ordinary Differential Equations (Stiff Problems and Boundary Value Problems), in Chinese Beijing: Higher Education Press, 1991, 1.
8. Li Ronghua, Weng Guochen, Numerical Methods in Differential Equations (in Chinese), 3rd ed., Beijing: Higher Education Press, 1996, 1.
9. Dahlquist, G., Convergence and stability in the numerical integration of ordinary differential equations, Math. Scandinavica, 1956, 4: 33.
10. Dahlquist, G., 33 years of numerical instability, Part I, BIT, 1985, 25: 188.
11. Heisenberg, W., The Physical Principles of Quantum Theory, Chicago: University of Chicago Press, 1930.
12. McMurry, S. M., Quantum Mechanics, London: Addison-Wesley Longman Ltd (reprined in China by Beijing World Publishing Corporation), 1998.