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標題: Lagrange,Divided Difference 多項式與 B-spline 函數及其應用
Lagrange,Divided Difference Polynomials and B-spline Functions and Their Applications
作者: 山澤棻
Shan, Tse-Fen
關鍵字: interpolating polynomials;內插多項式;B splines;B樣條
出版社: 應用數學系所
引用: References [1] H. N. Caglar, S. H. Caglar, AND E. H. Twizell, The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions, Int. J. Comput. Math. 71 (1999), no. 3, pp. 373{381. [2] Nazan Caglar, AND Hikmet Caglar B-spline solution of singular boundary value problems, Appl. Math. Comput. 182 (2006), no. 2, 1509{1513 [3] H. N. Caglar, S. H. Caglar , AND E.H. Twizell, The numerical solution of fth-order boundary- value problems with sixth-degree B-spline functions, Appl Math Lett 12 (1999), pp. 25{30 [4] K.N.S. Kasi Viswanadham, P. Murali Krishna a, AND C. Prabhakara Raob, Numerical So- lution of Fifth Order Boundary Value Problems by Collocation Method with Sixth Order B- Splines, Int. J. Appl. Sci. Eng., 2010. 8, 2: 119-125 [5] C. de Boor, A practical guide to splines , Springer-Verlag (1978). [6] Schatzman, M. , Numerical analysis : a mathematical introduction , Oxford University Press (2002). [7] Plybon, Benjamin F. , An introduction to applied numerical analysis , PWS-Kent Pub. Co., (1992). [8] Nurnberger, G. (Gunther), 1948, Approximation by spline functions , Springer-Verlag (1989). [9] Massopust, Peter Robert, 1958, Interpolation and approximation with splines and fractals , Oxford University Press (2010). [10] Kadalbajoo, M. K, AND Patidar, K. C Exponentially tted spline in compression for the numerical solution of singular perturbation problems, Comput. Math. Appl. 46 (2003), no. 5{6, 751{767 [11] Kadalbajoo, M. K, AND Arora, Puneet B-spline collocation method for the singular- perturbation problem using arti cial viscosity, Comput. Math. Appl. 57 (2009), no. 4, 650-663 [12] Prenter, P. M. 1989, Splines and Varia- tional Methods, John-Wiley and Sons, New York.
在本篇論文中, 我們將藉由內插多項式的定義來研究B-splines及使用colloction
方法藉由B-splines當做基底函數來解邊界值問題. 我們從B-splines的遞迴公式來
討論更多關於B-splines的性質. 我們也證明如何利用邊界條件來將過多的基底函數縮減. 然後我們給出了一個數值例子, 也在奇異擾動問題下發現數值解跟ε/h的關係.

In this thesis, we will recall the definition of polynomial interpolation to study the
properties of B-splines and use collocation method with B-splines as basis functions
for the numerical solutions of boundary value problems. We discuss the functions of
B-splines in detail starting from the recursion formula of B-splines. We provide the
procedure of reducing numbers of basis functions by boundary conditions. Third
order and fifth order boundary value problems are employed for applications. Then
we give s numerical experiment in last section and in two points singular perturbed
problems we find the relationship between the solutions and the ratio of h
其他識別: U0005-1807201115155400
Appears in Collections:應用數學系所

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