政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/90192
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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/90192


    Title: 縮基法初始值問題之數值研究
    Numerical studies of reduced basis methos for initial value problems
    Authors: 陳揚敏
    Contributors: 林美佑
    陳揚敏
    Keywords: 縮基法，投影法
    Reduced Basis Method, Projection
    Date: 1990
    1989
    Issue Date: 2016-05-03 14:17:47 (UTC+8)
    Abstract: 縮基法(RBM) 是對參數化的曲線求逼近解的一個方法，基本上乃使用投影法將解曲線投射到解空間的一子空間中，如此一來，可將原問題轉換成一較小的系統，並經由數值計算出小系統的解，來求得大系統的一逼近解。在本篇論文中主要的乃探討RBM在常微分方程組初始值問題上的應用，並發展一套含有誤差控制的演算法。
    The reduced basis method(RBM) is a scheme for approximating parametric solution curves. The basic technique of RBM is projection. By applying the method, we can find an approximate solution of the original system which satisfies a system of smaller size. In this paper, we mainly concern the applications of RBM for ODE initial value problems and develop an algorithm which contains a set of error controls.
    Reference: [1] N. N. Abdelmalek, Roundoff Error Analysis for Gram-Schmidt Method and Solution of Linear Least Squares Problems, BIT, 11(1971), pp.945-968.
    [2] B. O. Almroth, P. Stern and F. A. Brogan, Automatic Choice of Global Shape Functions in Structural Analysis, AIAA J., 16(1978), pp. 525-528.
    [3] E. Fehlberg, Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Warmeleitungsprobleme, Computing, 6(1970), pp. 61-71.
    [4] J. P. Fink and W. C. Rheinboldt, On the Discretization Error of Parametrized Nonlinear Equations, SIAM J. Numer. Anal., 20(1989),pp. 792-746.
    [5] J. P. Fink and W. C. Rheinboldt, On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations,Z. Angew. Math.Mech., 69(1989), pp. 21-28.
    [6] J . P. Fink and W. C. Rheinboldt, Local Error Estimates for Parametrized Nonlinear Equations, SIAM J. Numer. Anal., 22(1985),pp. 729-795.
    [7] C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, 1971, Prentice-Hall inc., Englewood Cliffs, New Jersey.
    [8] G. H. Golub and C. F. Van Loan, Matrix Computations, 1989.
    [9] M. K. Gordon and L. F. Shampine, Computer Solution of Ordinary Differential Equations, The Initial Value Problem, ~974, W. H. Freeman and Company, San Francisco.
    [10] J. D. Lambert, Computational Methods in Ordinary Differential Equations, 1989 J. W. Arrowsmith Ltd. Bristol.
    [11] M. Lin Lee, Estimation of the Error in the Reduced Basis Method Solution of Differential Algebraic Equation System, SIAM J. Numer. Anal., to appear.
    [12] M. Lin Lee, The Reduced Basis Method for Differential Algebraic Equation System, Technical Report ICMA-85-85, Inst. for Compo Math. And Appl., University of Pittsburgh, Pittsburgh, PA, July, 1985.
    [13] N. A. Nagy, Model Representation of Geometrically Nonlinear Behavior by the Finite Element Method, Computers and Structures,10(1977), pp. 689-688.
    [14] A. K. Noor and J. M. Peters, Reduced Basis Technique for Nonlinear Analysis of Structures, AIAA J., 18(1980), pp. 455-462.
    [15] A. K. Noor, C. M. Andersen and J. M. Peters, Reduced Basis Technique for Collapse of Shells, AIAA J., 19(1981), pp. 999-997.
    [16] T. A. Porsching, Estimation of the Error in the Reduced Basis Method Solution of Nonlinear Equations, Math. Comp., 45(1985), pp. 487-496.
    [17] T. A. Porsching and M. Lin Lee, The Reduced Basis Method For Initial Value Problems, SIAM J. Numer. Anal., 24(1987), pp. 1277-1287.
    [18] J. R. Rice, Experiments on Gram-Schmidt Orthogonalization, Math. Compo 20(1966), pp. 925-928.
    [19] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 1980,Springer, New York, Heidelberg, Berlin.
    [20] G. W. Steward, Introduction to Matrix Computation, 1979, Academic Press, New York and London.
    [21] G. W. Steward, Perturbation Bounds for the QR Factorization of a Matrix, SIAM J, Numer. Anal., 14(1977), pp. 509-518.
    [22] J. S. Vandergraft, Introduction to Numerical Computation, 1989,Automated Sciences Group, Inc., Silver Spring, Maryland.
    [23] R. E. Williamson, Introduction to Differential Equations, ODE, PDE and Series.
    Description: 碩士
    國立政治大學
    應用數學系
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002005457
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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