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研究生:羅佳瑋
研究生(外文):Jia-Wei Lo
論文名稱(外文):Pseudo-Transient Continuation as a Tool to Study Equilibria of ODE Systems
指導教授:卓建宏卓建宏引用關係
指導教授(外文):Chien-Hong Cho
口試委員:林敏雄洪宗乾
口試日期:2014-07-24
學位類別:碩士
校院名稱:國立中正大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:34
中文關鍵詞:擬短暫連續方法
外文關鍵詞:Pseudo-transient continuation
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In this paper we study the method of Pseudo-transient as a tool for solving some ODEs, PDEs or predator-prey system.
To compute the stationary solutions of PDEs or equilibria of ODEs numerically, we need to compute for a long time period to ensure that we have the approximation of the solutions at large time. In this paper, we would like to introduce Pseudo-transient method to speed up our computation if the procedure between the initial condition and behavior at large time is not important. We report several numerical results and compare the advantages and disadvantages for the Pseudo-transient method and the usual ODE solvers.
Contents
1 Introduction 1
2 Pseudo-transient continuation 1
3 Examples and Numerical experiments 3
3.1 An ODE system . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 A predator-prey model . . . . . . . . . . . . . . . . . . . . . . 6
3.3 The Burgers equation . . . . . . . . . . . . . . . . . . . . . . . 14
4 Conclusion 20
References 21
Appendix 22
References
[1] J. Burns, A. Balogh, D. S. Gilliam, and V. I. Shubov. Numerical stationary
solutions for a viscous Burgers’ equation. J. Math. Systems Estim.
Control, 8(2):16 pp. (electronic), 1998.
[2] G. J. Butler and Paul Waltman. Bifurcation from a limit cycle in a two
predator-one prey ecosystem modeled on a chemostat. J. Math. Biol.,
12(3):295–310, 1981.
[3] Chuang-Hsiung Chiu. Lyapunov functions for the global stability of competing
predators. J. Math. Anal. Appl., 230(1):232–241, 1999.
[4] S. B. Hsu, S. P. Hubbell, and Paul Waltman. Competing predators. SIAM
J. Appl. Math., 35(4):617–625, 1978.
[5] C. T. Kelley and David E. Keyes. Convergence analysis of pseudotransient
continuation. SIAM J. Numer. Anal., 35(2):508–523, 1998.
[6] C. T. Kelley, C. T. Miller, and M. D. Tocci. Termination of Newton/
chord iterations and the method of lines. SIAM J. Sci. Comput., 19(1):
280–290, 1998. Special issue on iterative methods (Copper Mountain,
CO, 1996).
[7] Torsten Lindström. Global stability of a model for competing predators:
an extension of the Ardito & Ricciardi Lyapunov function. Nonlinear
Anal., 39(6, Ser. A: Theory Methods):793–805, 2000.
[8] Wim A. Mulder and Bram van Leer. Experiments with implicit upwind
methods for the Euler equations. J. Comput. Phys., 59(2):232–246, 1985.
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