| dc.contributor.advisor | 蔡隆義 | zh_TW |
| dc.contributor.advisor | Tsai, Long-yi | en_US |
| dc.contributor.author (Authors) | 劉凱元 | zh_TW |
| dc.contributor.author (Authors) | Liu, Kai-yuan | en_US |
| dc.creator (作者) | 劉凱元 | zh_TW |
| dc.creator (作者) | Liu, Kai-yuan | en_US |
| dc.date (日期) | 2004 | en_US |
| dc.date.accessioned | 17-Sep-2009 13:49:30 (UTC+8) | - |
| dc.date.available | 17-Sep-2009 13:49:30 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Sep-2009 13:49:30 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0907510012 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32600 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 90751001 | zh_TW |
| dc.description (描述) | 93 | zh_TW |
| dc.description.abstract (摘要) | 在這篇論文中，我們探討了在任何正參數之下，范德波爾方程的極限環結果。藉由改良後的同倫擾動方法，我們求得了一些極限環的近似結果。相對於傳統的擾動方法，這種同倫方法在方程中並不受限於小的參數。除此之外，我們也設計了一個演算法來計算極限環的近似振幅及頻率。 | zh_TW |
| dc.description.abstract (摘要) | In this thesis, we study the limit cycle of van der Pol equation for parameter ε>0. We give some approximate results to the limit cycle by using the modified homotopy perturbation technique. In constract to the traditional perturbation methods, this homotopy method does not require a small parameter in the equation. Besides, we also devise a new algorithm to find the approximate amplitude and frequency of the limit cycle. | en_US |
| dc.description.tableofcontents | Section 1 Introduction......................................1Section 2 Existence and Uniqueness of Stable Limit Cycle....3Section 3 Some Traditional Perturbation Results.............6Section 4 Modified Homotopy Perturbation Method.............9Section 5 Numerical Comparison.............................27Section 6 Discussion and Open Problems.....................32References......................,..........................40Appendix...........................,.......................42 | zh_TW |
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| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0907510012 | en_US |
| dc.subject (關鍵詞) | 擾動法 | zh_TW |
| dc.subject (關鍵詞) | 同倫 | zh_TW |
| dc.subject (關鍵詞) | 范德波爾方程 | zh_TW |
| dc.subject (關鍵詞) | Perturbation Method | en_US |
| dc.subject (關鍵詞) | Homotopy | en_US |
| dc.subject (關鍵詞) | Van Der Pol Equation | en_US |
| dc.title (題名) | 同倫擾動法對於范德波爾方程的研究 | zh_TW |
| dc.title (題名) | Homotopy Perturbation Method for Van Der Pol Equation | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] Andersen, C.M. and J.F. Geer, Power series expansions for the frequency and period of the limit cycle of the van der Pol equation, SIAM Journal on Applied Mathematics 42, pp. 678-693, (1982). | zh_TW |
| dc.relation.reference (參考文獻) | [2] Buonomo, A., The periodic solution of van der Pol`s equation, SIAM Journal on Applied Mathematics 59, 1, pp156-171, (1998). | zh_TW |
| dc.relation.reference (參考文獻) | [3] Dadfar, M.B., J. Geer, and C.M. Andersen, Perturbation analysis of the limit cycle of the free van der Pol equation, SIAM Journal on Applied Mathematics 44, pp. 881-895, (1984). | zh_TW |
| dc.relation.reference (參考文獻) | [4] Ferdinand Verhulst, Nonlinear differential equations and dynamical systems, Springer-Verlag Berlin Heidelberg New York, (1996). | zh_TW |
| dc.relation.reference (參考文獻) | [5] He, J.H., Homotopy perturbation technique, Computer Methods in Applied Mechanics Engineering 178, pp.257-262, (1999). | zh_TW |
| dc.relation.reference (參考文獻) | [6] He, J.H., Modified Lindstedt-Poincare methods for some strongly non-linear oscillations Part I: expansion of a constant, International Journal of Non-Linear Mechanics 37, pp. 309 -314, (2002). | zh_TW |
| dc.relation.reference (參考文獻) | [7] He, J,H, Modified Lindstedt Poincar□ methods for some strongly non-linear oscillations Part II: a new transformation, International Journal of Non-Linear Mechanics 37, pp. 315-320, (2002). | zh_TW |
| dc.relation.reference (參考文獻) | [8] He, J.H., Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation 135, pp. 73-79, (2003). | zh_TW |
| dc.relation.reference (參考文獻) | [9] Liao, S.J., An approximate solution technique not depending on small parameters: a special example, International Journal of Nonlinear Mechanics 30, 371-380, (1995). | zh_TW |
| dc.relation.reference (參考文獻) | [10] Li□nard, A.M., □tude des oscillations entretenues, Revue G□n□rale de l`□lectricit□ 23, pp. 901-912 and pp. 946-954, (1928). | zh_TW |
| dc.relation.reference (參考文獻) | [11] Lin, C.C., Mathematics applicated to deterministic problems in natural sciences, Macmillan, New York, (1974). | zh_TW |
| dc.relation.reference (參考文獻) | [12] 劉秉正, 非線性動力學與混沌基礎, 徐氏基金會, (1998). | zh_TW |
| dc.relation.reference (參考文獻) | [13] Nayfeh, A.H., Introduction to Perturbation Techniques, Wiley, New York, (1981). | zh_TW |
| dc.relation.reference (參考文獻) | [14] Nayfeh, A.H., Problems in Perturbation, Wiley, New York, (1985). | zh_TW |
| dc.relation.reference (參考文獻) | [15] Ronald. E. Mickens. An Introduction to Nonlinear Oscillations, Combridge University Press, (1981). | zh_TW |
| dc.relation.reference (參考文獻) | [16] Shih, S.D., On periodic orbits of relaxation oscillations, Taiwanese Journal of Mathematics 6, 2, pp. 205-234, (2002). | zh_TW |
| dc.relation.reference (參考文獻) | [17] Van der Pol, B., On "relaxation-oscillations," Philosophical Magazine, 2, pp. 978-992, (1926) | zh_TW |
| dc.relation.reference (參考文獻) | [18] Urabe, M., Periodic solutions of van der Pol`s equation with damping coefficient λ = 0 - 10, IEEE Transactions Circuit Theory, CT-7, pp. 382--386, (1960). | zh_TW |
