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研究生:簡正傑
研究生(外文):Cheng-Chieh Chien
論文名稱:圓盤上Poisson方程近似值的誤差估計
論文名稱(外文):The error estimate for approximation of Poisson equation on a disk
指導教授:郭紅珠
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:34
中文關鍵詞:圓盤誤差估計
外文關鍵詞:error estimatePoisson equationdisk
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  • 被引用被引用:0
  • 點閱點閱:149
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這篇論文的主要目的在於建立圓盤上Poisson方程的離散型極大值原理。我們從極大值原理繼續建立期望區域的收斂速度,然後得到圓盤上 Poisson 方程近似值的誤差估計。
The purpose of this work is devoted to establishing the discrete maximum principle for discrete Poisson equation on a polar disk. We proceed from the maximum principle to establish the desired bound of convergence rate. The error estimate for approximation of Poisson equation on a disk is then established.
CONTENTS
1. Introduction..........................................1
2. Finite Difference Discretization...............2
3. The Discrete Maximum Principle..........13
4. The Error Estimates............................31
5. References.........................................34
FIGURES
1. Figure2.1..............................................9
2. Figure3.1............................................13
[1] A. D. Aleksandrov, Uniqueness conditions and estimates for the solution of the Dirichlet problem, Vestnil Leningrad. Univ. 18 (1963), no. 3, 5-29; English transl, Amer. Math. Soc. Transl. (2) 68 (1968), 89-119.
[2] J. Ya. Bakel'' man, Theory of quasilinear elliptic equations, Sibirsk. Mat. Zn. 2 (1961), 179-186.
[3] A. Bayliss, M. Gunzburger and E. Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J. Appl. Math. vol 42, No 2, 430-451, (1982).
[4] D.Gilbarg and N.S.Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1983.
[5] H. J. Kuo abd N.S.Trudinger, Linear elliptic difference inequalities with randon coefficients, Math Comp. 55(1990), 37-53.
[6] H. J. Kuo abd N.S.Trudinger, Positive difference operators on general meshes, Duke Mathematical Journal, vol. 83(1996), 415-433.
[7] M. C. Lai, A note on finite difference discretizations for Poisson equation on a disk, Numerical Methods for Partial Differential Equations, vol 17, issue 3, 199-203, (2001).
[8] M. C. Lai, Z. Li and X. Lin, Fast solvers for 3D Poisson equations involving interfaces in a finite or the infinite domain, Journal of Computational and Applied Mathematics , vol 191, 106-125, (2006).
[9] R. Dautray and J.-L. Lions. Mathematical analysis and numerical methods for science and technology. vol. 1, 264 265, Springer-Verlag, Berlin, (1988).
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