研究生: |
陳怡杏 |
---|---|
論文名稱: |
一個化學熱質轉換模型分歧問題之數值探討 The Numerical Investigation of bifurcation problems in a chemical heat and mass transfer model |
指導教授: | 簡國清 |
口試委員: | |
學位類別: |
碩士 Master |
系所名稱: |
|
論文出版年: | 2005 |
畢業學年度: | 94 |
語文別: | 中文 |
論文頁數: | 99 |
中文關鍵詞: | 分歧點 、隱函數定理 、打靶法 、牛頓迭代法 、解分支 、割線猜測法 、虛擬弧長延拓法 |
外文關鍵詞: | Bifurcation point, Implicit function theorem, Shooting method, Newton’s iterative method, Solution branches, Secant predictor, Pseudo-arclength continuation algorithm |
相關次數: | 點閱:3 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本論文旨在數值探討一個化學熱質轉換模型的分歧問題.
首先,我們以隱函數定理為基礎,推導計算出分歧點,再利用打靶法,牛頓迭代法,虛擬弧長延拓法及割線猜測法等數值方法,來延拓出所有通過分歧點的解分支路徑.
最後,我們藉由改變各種參數,觀察解路徑上的分歧現象與分歧點的變化.
The purpose of this paper is to numerically investigate bifurcation problems in a chemical heat and mass transfer model.
First, we base on implicit function theorem to calculate the bifurcation points and then get the path of all that passing through the bifurcation points with the shooting method, Newton’s iterative method, Pseudo-arclength continuation method and secant predictor and so on.
Finally, we observe bifurcation phenomenons at bifurcation points with different parameters.
參考文獻
[1] Aselone,P.M. and Moore,R.H., An Extension of the Newton-Kantorovich Method for Sloving Nonlinear Equations with An Application to Elasticity. J. Math. Anal. l3, pp.476-501,1966.
[2] Bauer,L., Reiss,E.L., and Keller,H.B., Axisymmetric Bucking of Hollow Spheres and hemispheres, Comm. Pure Appl. Math., 23, 1970.
[3] B. Bunow and J. P. Kernevez, Numerical exploration of bifurcating branches of solutions to reaction-diffusion equations from immobilized enzyme kinetics, to appear.
[4] Choi,Y.S., Jen,K,C.,(簡國清) and McKenna,P.J., The Structure of the Solution Set for Periodic Oscillations in a Suspension Bridge Model, IMA J. Appl. Math., 47, 1991.
[5] Crandall, M.G. and Rabinowitz, P.H., Bifurcation from simple eigenvalue, J. Funct. Anal., 1971.
[6] Crandall, M. G. and Rabinowliz, P. H., Mathematical Theory of Bifurcation, Bifurcation Phenomena in Mathematical Physics and Related Topics, edit by Bardos, C. and Bessis, D., NATO Advanced Study Institute Series, 1979.
[7] Crandall, M. G., An Introduction to Constructive Aspects of Bifurcation and The Implicit Function Theorem, Application of Bifurcation Theorem, edited by P. H. Rabinowtiz, Academic Press,New York,1977.
[8] D. W. Decker and H. B. Keller, Solution branching—A constructive technique, in New Approaches to Nonlinear Problems in Dynamics (P. J. Holmes, Ed.) SIAM Publ., Philadelphia, 1980.
[9] G. Iooss and D. Joseph. Elementary stability and bifurcation theory, Springer Verlag, New York, 1980.
[10] H. B. keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in Applications of Bifurcation Theory, (P. H. Rabinowitz, Ed.) Academic, New York, 1977.
[11] I. Stakgold, Branching of solutions of nonlinear equations, SIAM Rev. 1971.
[12] Jepson A.D. and Spence A., Numerical Methods for Bifurcation Problems, State of the Art in NUmeriacI Analysis, edit bu A, lserles, MJD Powell,1987.
[13] Jen,K.C.(簡國清), The Stability and Convergence of a Crank- Nicolson Scheme for a Nonlinear Beam Vibration Equation, Chinese Journal of Mathematics, Vol.23, No.2, 1995.
[14] Keller, H.B. and Langford, W.F., Iterations, perturbations and multiplicities for non-linear bifurcation problems, Arch. Rational Mech. Anal., 48,1972.
[15] Keller, H.B., Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems, Applications of Bifurcation Theory, Edited by Rabinowitz, P. H., Academic Press,1977.
[16] Keller, H. B., Lectures on Numerical Methods in Bifurcation Problems, TATA Institute of Fundamental Research, Springer-Verlag,1987.
[17] Kupper, T., Mittelmann, H. D. and Weber, H. (eds.), Numerical Methods for Bifurcation Problems, Birkhauser, Basel.1984.
[18] Kubicek, M. and Marek, M., Computational Merhods in Bifurcation Theory and Dissipative Structures, Springer-Verlag, New York.1983.
[19] L. Bauer, H. B. Keller, and E. L. Reiss, Multiple eigenvalues lead to secondary bifurcation, SIAM Rev,1975.
[20] M. G. Grandal, An introduction to constructive aspects of bifurcation and the implicit function theorem in Applications of Bifurcation Theory, (T. H. Rabinowitz, Ed.) Academic, New York,1977.
[21] M. Kubicek, Dependence of solution of nonlinear systems on a parameter, A.C.M. Trans. Math. Software,1976.
[22] M. Kubicek and M. Marek, Evaluation of limit and bifurcation points for algebraic and nonlinear boundary value problems, Appl. Math. Comput.1979.
[23] M. Kubicek and V. Hlavacek, General parameter mapping technique—a procedure for solution of non-linear boundary value problems depending on an actual parameter , J. Inst. Math. App. 12 ,1973.
[24] M. Kubicek and V. Hlavacek, Solution of nonlinear boundary value problems—Va and Vb. A novel method: general parameter mapping (GPM) and predictor-corrector GPM method, Chem. Eng. Sci. 27 ,1972.
[25] Rheinboldt, W. C., Solution Fields of Nonlinear Equations and Continuation Methods, SIAM J. Numer. Anal., 17,1980.
[26] T. L. Saaty and J. Bram, Non-linear Mathematics, McGraw-Hill, New York,1964.
[27] V. Hlavacek, M. Marek and M. Kubicek, Modeling of chemical reactors—X.Multiple solutions of enthalpy and mass balances for a catalytic reaction within a porous catalyst particle, Chem, Eng. Sci. 23,1968.
[28] Wacker, H.(ed-), Continuation Methods, Academic Press, New York,1978.
[29] W. C. Rheinboldt and J. V. Burkardt, A program for a locally-parameterized continuation process, Technical Report ICMA-81-30, Inst. For Comput. Math. and Appl. Univ. of Pittsburgh,1981.
[30]黃治平,非線性代數方程組分歧點與解分支之探討,新竹教育大學碩士論文,2004.
[31]林慧芬,非線性邊界值問題分歧點計算及其解路徑延拓,新竹教育大學碩士論文,2005.