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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/32600
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dc.contributor.advisor蔡隆義zh_TW
dc.contributor.advisorTsai, Long-yien_US
dc.contributor.author劉凱元zh_TW
dc.contributor.authorLiu, Kai-yuanen_US
dc.creator劉凱元zh_TW
dc.creatorLiu, Kai-yuanen_US
dc.date2004en_US
dc.date.accessioned2009-09-17T05:49:30Z-
dc.date.available2009-09-17T05:49:30Z-
dc.date.issued2009-09-17T05:49:30Z-
dc.identifierG0907510012en_US
dc.identifier.urihttps://nccur.lib.nccu.edu.tw/handle/140.119/32600-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學研究所zh_TW
dc.description90751001zh_TW
dc.description93zh_TW
dc.description.abstract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。\n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.abstractIn 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.tableofcontentsSection 1 Introduction......................................1\nSection 2 Existence and Uniqueness of Stable Limit Cycle....3\nSection 3 Some Traditional Perturbation Results.............6\nSection 4 Modified Homotopy Perturbation Method.............9\nSection 5 Numerical Comparison.............................27\nSection 6 Discussion and Open Problems.....................32\nReferences......................,..........................40\nAppendix...........................,.......................42zh_TW
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dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0907510012en_US
dc.subject擾動法zh_TW
dc.subject同倫zh_TW
dc.subject范德波爾方程zh_TW
dc.subjectPerturbation Methoden_US
dc.subjectHomotopyen_US
dc.subjectVan Der Pol Equationen_US
dc.title同倫擾動法對於范德波爾方程的研究zh_TW
dc.titleHomotopy Perturbation Method for Van Der Pol Equationen_US
dc.typethesisen
dc.relation.reference[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[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[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[4] Ferdinand Verhulst, Nonlinear differential equations and dynamical systems, Springer-Verlag Berlin Heidelberg New York, (1996).zh_TW
dc.relation.reference[5] He, J.H., Homotopy perturbation technique, Computer Methods in Applied Mechanics Engineering 178, pp.257-262, (1999).zh_TW
dc.relation.reference[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[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[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[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[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[11] Lin, C.C., Mathematics applicated to deterministic problems in natural sciences, Macmillan, New York, (1974).zh_TW
dc.relation.reference[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[13] Nayfeh, A.H., Introduction to Perturbation Techniques, Wiley, New York, (1981).zh_TW
dc.relation.reference[14] Nayfeh, A.H., Problems in Perturbation, Wiley, New York, (1985).zh_TW
dc.relation.reference[15] Ronald. E. Mickens. An Introduction to Nonlinear Oscillations, Combridge University Press, (1981).zh_TW
dc.relation.reference[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[17] Van der Pol, B., On \"relaxation-oscillations,\" Philosophical Magazine, 2, pp. 978-992, (1926)zh_TW
dc.relation.reference[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
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