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研究生:李芳雯
研究生(外文):Fang-wen Li
論文名稱:用徑向函數配置法求解奇異擾動偏微分方程
論文名稱(外文):Radial Basis Collocation Method for Singularly Perturbed Partial Differential Equations
指導教授:李子才
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
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:2004
畢業學年度:92
語文別:英文
論文頁數:34
中文關鍵詞:徑向函數配置法奇異擾動偏微分方程
外文關鍵詞:radial basis collocation method
相關次數:
  • 被引用被引用:0
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  • 下載下載:5
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本篇論文簡介徑向函數配置法,並用此方法求解奇異擾動偏微分方程。在文章的最後,提供幾個數值結果,當奇異擾動偏微分方程的參數等於10的負7次方。
In this thesis, we integrate the particular solutions of singularly perturbed partial differential equations into radial basis collocation method to solve two kinds of boundary layer problem.
Chap 1. Introduction
Chap 2. Radial Basis Collocation Method
Chap 2.1. Description of Radial Basis Collocation Method
Chap 2.2. Erroe Estimation
Chap 3. Numberical Experiment
Chap 3.1. Model I
Chap 3.2. Model IA
Chap 3.3. Model IB
Chap 3.4. Model II
Chap 3.5 The Schwartz Alternating Method
Chap 3.6 The Combined Method
Chap 4. Conclusion
[1]Hsin-Yu Hu, Zi-Cai Li, and A. H. D. Cheng, Radial basis
collocation method for elliptic boundary value problem, accepted by Inter J. Computers & Mathematics with application.
[2]Hsin-Yu Hu, Heng-Shuing Tsai, Zi-Cai Li, and S. Wang, Particular solutions of singularly pertubed partial differential equations with constant coefficients in rectangular domains, Part II. computational aspects, Technical report, Department of Applied Mathematics, National Sun Yat-sen University, 2004, submitted.
[3]H. Y. Hu, and Z. C. Li, Combinations of collocation and
finite element methods for Poisson''s equation, Technical report, Department of Applied Mathematics, National Sun Yat-sen University, 2003.
[4]J. J. H. Miller, E. O''Riordan and G. T. Shishkin, Fitted
Numerical Methods for Singular Pertubation Problems, Error
Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions, World Scientific, Singapore, 1996.
[5]R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. of Geophysical Research, Vol. 76, pp.1905-1915, 1971.
[6]R. Franke, Scattered data interpolation tests of some
methods, Math. Comp. Vol. 38, pp. 181-200, 1982.
[7]R. Franke and R. Schaback, Solving partial differential
equations by collocation using radial functions, Applied
Mathematics and Computation, Vol. 93, pp. 73-82, 1998.
[8]M. Golberg, Recent developments in the numerical evaluation of partial solutions in the boundary element methods, Applied Mathematics and Computation Vol. 75, pp. 91-101, 1996.
[9]E. J. Kansa, Multiqudrics - A scattered data approximation scheme with applications to computational fluid-dynamics - I Surface approximations and partial derivatives, Computer Math. Applic., Vol. 19, No.8/9, pp. 127-145, 1992.
[10]E. J. Kansa, Multiqudrics - A scattered data approximation scheme with applications to computational fluid-dynamics - II Solutions to parabolic, hyperbolic and elliptic partial differential equations, Computer Math. Applic., Vol. 19, No.8/9, pp. 147-161, 1992.
[11]W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions, II., Math. Comp. Vol. 54, pp. 211-230, 1990.
[12]Z. Wu and R. Schaback, Local error estimates for radial
basis function interpolation of scattered data, IMA J. of Numer. Anal. Vol. 13, pp. 13-27, 1993.
[13]J. Yoon, Local error estimates for radial basis function interpolation of scattered data, J. Approx. Theory, Vol. 112, No. 1, pp. 1-15, 2001.
[14]P. G. Ciarlet, Basic error estimates for elliptic problems, in Eds., P.G. Ciarlet and J. L. Lions, Finite Element Methods (Part I), pp. 17-352, North-Holland, 1991.
[15]Hsin-Yu Hu and Zi-Cai Li, Collocation Method for Poisson''s Equation , Technical report, Department of Applied Mathematics, National Sun Yat-sen University, 2002, submitted.
[16]A. H. D. Cheng, M.A. Golberg, E. J. Kansa and G. Zammito, Exponential convergence and H-c multiquadrics collocation method for partial differential equations, Numer. Methods Partial Differential Equations, Vol. 19, No. 5, pp. 571-594, 2003.
[17]Zi-Cai Li, Hen-Shuing Tsai, S. Wang and J. J. H. Miller, New models of singularly perturbed differential equations with waterfalls solutions, Technical report, Department of Applied Mathematics, National Sun Yat-sen University, 2004, submitted.
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