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Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079000

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References:


[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