Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems
Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.
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44FD3DG-2/2/c59d6272888f882a64514091fff104dc
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http://comjnl.oxfordjournals.org/cgi/content/abstract/12/2/151
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methods which applied to two-point boundary value problems," Applied
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(Online). Available: http://www.sciencedirect.com/science/article/B6TY8-
4H74KY7-1/2/60f26c55f79c0a39775e1d76586975da
[7] G. Xu and G.-Z. Wang, "Extended cubic uniform
b-spline and (alpha)-b-spline," Acta Automatica Sinica,
vol. 34, no. 8, pp. 980-984, Aug. 2008. (Online).
Available: http://www.sciencedirect.com/science/article/B8H0V-
4T6VT15-3/2/7c4718af9afe2c6bae6b0d1d4f8e66e3
[1] R. L. Burden and J. D. Faires, Numerical Analysis, 8th ed. Brooks/Cole,
Cengage Learning, 2005, pp. 641-647, 649-654, 656-660, 662-667, 668-
682, 684-685.
[2] Q. Fang, T. Tsuchiya, and T. Yamamoto, "Finite difference,
finite element and finite volume methods applied to two-point
boundary value problems," Journal of Computational and Applied
Mathematics, vol. 139, no. 1, pp. 9 - 19, 2002. (Online).
Available: http://www.sciencedirect.com/science/article/B6TYH-
44FD3DG-2/2/c59d6272888f882a64514091fff104dc
[3] W. G. Bickley, "Piecewise cubic interpolation and
two-point boundary problems," The Computer Journal,
vol. 11, no. 2, pp. 206-208, 1968. (Online). Available:
http://comjnl.oxfordjournals.org/cgi/content/abstract/11/2/206
[4] E. L. Albasiny and W. D. Hoskins, "Cubic spline solutions
to two-point boundary value problems," The Computer Journal,
vol. 12, no. 2, pp. 151-153, 1969. (Online). Available:
http://comjnl.oxfordjournals.org/cgi/content/abstract/12/2/151
[5] D. J. Fyfe, "The use of cubic splines in the solution of
two-point boundary value problems," The Computer Journal,
vol. 12, no. 2, pp. 188-192, 1969. (Online). Available:
http://comjnl.oxfordjournals.org/cgi/content/abstract/12/2/188
[6] H. Caglar, N. Caglar, and K. Elfaituri, "B-spline interpolation
compared with finite difference, finite element and finite volume
methods which applied to two-point boundary value problems," Applied
Mathematics and Computation, vol. 175, no. 1, pp. 72 - 79, 2006.
(Online). Available: http://www.sciencedirect.com/science/article/B6TY8-
4H74KY7-1/2/60f26c55f79c0a39775e1d76586975da
[7] G. Xu and G.-Z. Wang, "Extended cubic uniform
b-spline and (alpha)-b-spline," Acta Automatica Sinica,
vol. 34, no. 8, pp. 980-984, Aug. 2008. (Online).
Available: http://www.sciencedirect.com/science/article/B8H0V-
4T6VT15-3/2/7c4718af9afe2c6bae6b0d1d4f8e66e3
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61360", author = "Nur Nadiah Abd Hamid and Ahmad Abd. Majid and Ahmad Izani Md. Ismail", title = "Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems", abstract = "Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.
", keywords = "two-point boundary value problem, B-spline, extendedcubic B-spline.", volume = "4", number = "2", pages = "294-3", }
