# 臺灣博碩士論文加值系統

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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. IntroductionChap 2. Radial Basis Collocation MethodChap 2.1. Description of Radial Basis Collocation MethodChap 2.2. Erroe EstimationChap 3. Numberical ExperimentChap 3.1. Model IChap 3.2. Model IAChap 3.3. Model IBChap 3.4. Model IIChap 3.5 The Schwartz Alternating MethodChap 3.6 The Combined MethodChap 4. Conclusion
 [1]Hsin-Yu Hu, Zi-Cai Li, and A. H. D. Cheng, Radial basiscollocation 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 andfinite 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, FittedNumerical Methods for Singular Pertubation Problems, ErrorEstimates 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 somemethods, Math. Comp. Vol. 38, pp. 181-200, 1982.[7]R. Franke and R. Schaback, Solving partial differentialequations by collocation using radial functions, AppliedMathematics 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 radialbasis 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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 1 橢圓型方程的Trefftz及Collocation法 2 邊界層與重調和邊界值問題解析解的研究 3 利用傅立葉配置法求解橢圓及特徵值問題 4 關於隨機股價之選擇權價值之有限體積法 5 Black-Scholes公式及其推導 6 低轉速平面發電機研究 7 熱效應於銅銲線接合製程之有限元素法模擬 8 高爾夫球桿頭撞擊聲音之分析 9 雷射熱破裂技術於切割脆性材料之模擬分析 10 薄板壓延之有限元素分析及擴寬預測式之決定 11 碳纖維高爾夫球桿之動態分析 12 高爾夫球桿頭結構重心變化之撞擊分析 13 小彎曲半徑迴轉拉彎成形之有限元素分析與製程設計 14 以小波轉換分析改善導波於複雜管線特徵之檢測 15 應用時間反轉法聚焦蘭姆波於缺陷檢測

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