P-stable linear symmetric multistep methods for periodic initial-value problems

Computer Physics Communications

Volumn 171, Issue 3, 2005, Pages 162-174

  Wang, Zhongcheng ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Multistep method; Numerical solution to the Duffing equation; P stable; Second order initial value problem with periodic solutions; Stiefel and Bettis problem

Indexed keywords

LINEAR SYSTEMS; NUMERICAL METHODS;

MULTISTEP METHODS; NUMERICAL SOLUTION TO THE DUFFING EQUATIONS; P-STABLE; SECOND-ORDER INITIAL VALUE PROBLEM WITH PERIODIC SOLUTIONS; STIEFEL AND BETTIS PROBLEMS;

INITIAL VALUE PROBLEMS;

EID: 24644444204     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2005.05.004     Document Type: Article

References (33)

1. A.C. Allison J. Comput. Phys. 6 1970 378
2. L. Landau, and E. Lifshitz Quantum Mechanics 1974 Pergamon Press Oxford
3. R.E. Mickens An Introduction to Nonlinear Oscillations 1981 Cambridge University Press New York
4. G.D. Quinlan, and S. Tremaine Astron. J. 100 1990 1694
5. G.D. Quinlan Resonances and instabilities in symmetric multistep methods astro-ph/9901136 1999
6. J.D. Lambert, and I.A. Watson J. Inst. Math. Appl. 18 1976 189
7. G. Psihoyios, and T.E. Simos New Astron. 8 2003 679 690
8. E. Stiefel, and D.G. Bettis Numer. Math. 13 1969 154
9. R. van Dooren J. Comput. Phys. 16 1974 186
10. E. Hairer Numer. Math. 32 1979 373
11. B. Neta, and T. Fukushima Comput. Math. Appl. 45 2003 383
12. J.R. Cash Numer. Math. 37 1981 355
13. U. Ananthakrishnaiah Math. Comp. 49 1987 553
14. T.E. Simos, and A.D. Raptis Computing 45 1990 175
15. A.D. Raptis, and T.E. Simos BIT 31 1991 160
16. T.E. Simos Proc. Roy. Soc. London A 6 1993 283
17. G. Avdelas, and T.E. Simos J. Comput. Appl. Math. 72 1996 345
18. T.E. Simos, and Ch. Tsitouras J. Comput. Phys. 130 1997 123
19. T.E. Simos Phys. Scripta 55 1997 644
20. G. Avdelas, and T.E. Simos Comput. Chem. 25 2001 3
21. T.E. Simos, and P.S. Williams Comput. Chem. 23 1999 513
22. T.E. Simos A. Hinchliffe Atomic Structure Computations in Chemical Modelling: Applications and Theory 2000 The Royal Society of Chemistry 38 142
23. T.E. Simos A. Hinchliffe Numerical Methods for 1D, 2D and 3D Differential Equations Arising in Chemical Problems in Chemical Modelling: Applications and Theory vol. 2 2002 The Royal Society of Chemistry 170 270
24. T.E. Simos A. Hinchliffe Numerical Methods in Chemistry in Chemical Modelling: Applications and Theory vol. 2 2004 The Royal Society of Chemistry 271 378
25. Z. Wang, and Y. Dai N. Math. J. Chin. Univ. 12 Suppl. 2003 146 150
26. Z. Wang, and Y. Dai Int. J. Modern Phys. C 14 2003 1087
27. Z. Wang, Y. Ge, Y. Dai, and D. Zhao A Mathematica program for the two-step twelfth-order method with multi-derivative for the numerical solution of a one-dimensional Schrödinger equation Comput. Phys. Comm. 160 1 2004 23 45
28. Y. Dai, Z. Wang, D. Zhao, and X. Song Comput. Phys. Comm. 165 2005 110
29. Z. Wang A new effective algorithm for the resonant state of a Schrödinger equation Comput. Phys. Comm. 167 1 2005 1
30. Z. Wang, D. Zhao, Y. Dai, D. Wu, An improved trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems, Proc. Roy. Soc. London A (2005), in press
31. D. Zhao, Z. Wang, and Y. Dai Importance of the first-order derivative formula in the Obrechkoff method Comput. Phys. Comm. 167 2 2005 65
32. D. Zhao, Z. Wang, Y. Dai, Y. Wang, A high-accurate and efficient Obrechkoff five-step method for undamped Duffing's equation, Int. J. Modern Phys. C (2005), in press
33. Y. Dai, Z. Wang, D. Wu, A four-step trigonometric fitted P-stable Obrechkoff method for periodic initial-value problems, J. Comput. Appl. Math. (2005), in press