Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two
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Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two

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

Abstract:

Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline interpolation method (CTBIM). Cubic trigonometric B-spline is a piecewise function consisting of trigonometric equations. This method is tested on some problems and the results are compared with cubic B-spline interpolation method (CBIM) from the literature. CTBIM is found to approximate the solution slightly more accurately than CBIM if the problems are trigonometric.

Keywords: trigonometric B-spline, two-point boundary valueproblem, spline interpolation, cubic spline

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081989

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References:


[1] R. L. Burden and J. D. Faires, Numerical Analysis. Belmont, CA: Brooks/Cole, 2005, 8th ed., pp. 641-642, 675.
[2] R. P. Agarwal, Boundary Value Problems for Higher Order Differential Equations). Singapore: World Scientific Publishin Co Pte Ltd., 1986, pp. 89-104.
[3] 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, issue 1, pp. 72-79, 2006.
[4] W. G. Bickley, "Piecewise cubic interpolation and two-point boundary problems," The Computer Journal, vol. 11, issue 2, pp. 206-208, 1968.
[5] E. L. Albasiny and W. D. Hoskins, "Cubic spline solutions to two-point boundary value problems," The Computer Journal, vol. 12, issue 2, pp. 151-153, 1969.
[6] D. J. Fyfe, "The use of cubic splines in the solution of two-point boundary value problems," The Computer Journal, vol. 12, issue 2, pp. 188-192, 1969.
[7] E. Al-Said, "Cubic spline method for solving two-point boundary value problems," Journal of Applied Mathematics and Computing, vol. 5, issue 3, pp. 669-680, 1998.
[8] A. Khan, "Parametric cubic spline solution of two point boundary value problems," Applied Mathematics and Computation, vol. 154, issue 1, pp. 175-182, 2004.
[9] P. Koch, T. Lyche, M. Neamtu and L. Schumaker, "Control curves and knot insertion for trigonometric splines," Advances in Computational Mathematics, vol. 3, issue 4, pp. 405-424, 1995.
[10] A. Nikolis, "Numerical solutions of ordinary differential equations with quadratic trigonometric splines," Applied Mathematics E-Notes, vol. 4, pp. 142-149, 1995.
[11] G. Walz, "Identities for trigonometric B-splines with an application to curve design," BIT Numerical Mathematics, vol. 37, issue 1, pp. 189- 201, 1997.
[12] N. S. Asaithambi, Numerical Analysis. Theory and Practice. Orlando, FL: Sauders College Publishing, 1995, pp. 361-373, 557, 724-761, 770.
[13] N. N. Abd Hamid, A. Abd. Majid, A. I. Md. Ismail, "Extended cubic Bspline interpolation method applied to linear two-point boundary value problems," World Academy of Science, Engineering and Technology (WASET), vol. 62, pp. 1663-1668, February 2010.
[14] G. Xu and G.-Z. Wang, "Extended cubic uniform B-spline and
[alpha]- B-spline.," Acta Automatica Sinica, vol. 34, issue 8, pp. 980-984, 2008.