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https://ah.lib.nccu.edu.tw/handle/140.119/90192| 題名: | 縮基法初始值問題之數值研究 Numerical studies of reduced basis methos for initial value problems |
作者: | 陳揚敏 | 貢獻者: | 林美佑 陳揚敏 |
關鍵詞: | 縮基法，投影法 Reduced Basis Method, Projection |
日期: | 1990 | 上傳時間: | 3-May-2016 | 摘要: | 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. |
參考文獻: | [1] N. N. Abdelmalek, Roundoff Error Analysis for Gram-Schmidt Method and Solution of Linear Least Squares Problems, BIT, 11(1971), pp.945-968.\r\n[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.\r\n[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.\r\n[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.\r\n[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.\r\n[6] J . P. Fink and W. C. Rheinboldt, Local Error Estimates for Parametrized Nonlinear Equations, SIAM J. Numer. Anal., 22(1985),pp. 729-795.\r\n[7] C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, 1971, Prentice-Hall inc., Englewood Cliffs, New Jersey.\r\n[8] G. H. Golub and C. F. Van Loan, Matrix Computations, 1989.\r\n[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.\r\n[10] J. D. Lambert, Computational Methods in Ordinary Differential Equations, 1989 J. W. Arrowsmith Ltd. Bristol.\r\n[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.\r\n[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.\r\n[13] N. A. Nagy, Model Representation of Geometrically Nonlinear Behavior by the Finite Element Method, Computers and Structures,10(1977), pp. 689-688.\r\n[14] A. K. Noor and J. M. Peters, Reduced Basis Technique for Nonlinear Analysis of Structures, AIAA J., 18(1980), pp. 455-462.\r\n[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.\r\n[16] T. A. Porsching, Estimation of the Error in the Reduced Basis Method Solution of Nonlinear Equations, Math. Comp., 45(1985), pp. 487-496.\r\n[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.\r\n[18] J. R. Rice, Experiments on Gram-Schmidt Orthogonalization, Math. Compo 20(1966), pp. 925-928.\r\n[19] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 1980,Springer, New York, Heidelberg, Berlin.\r\n[20] G. W. Steward, Introduction to Matrix Computation, 1979, Academic Press, New York and London.\r\n[21] G. W. Steward, Perturbation Bounds for the QR Factorization of a Matrix, SIAM J, Numer. Anal., 14(1977), pp. 509-518.\r\n[22] J. S. Vandergraft, Introduction to Numerical Computation, 1989,Automated Sciences Group, Inc., Silver Spring, Maryland.\r\n[23] R. E. Williamson, Introduction to Differential Equations, ODE, PDE and Series. | 描述: | 碩士 國立政治大學 應用數學系 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#B2002005457 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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