Document Type: Research Paper

Authors

1 Department of Statistics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran.

2 Department of Mathematics, Faculty of Science, Technical and Vocational University(TVU), Tehran, Iran and Department of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 57166-17165, Urmia-Iran.

3 Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.

4 Department of Mathematics, Faculty of Science, Urmia University of technology, P.O.Box 57166-17165, Urmia, Iran.

Abstract

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is discussed. The interpolation errors are studied. Numerical results illustrate the efficiency and effectiveness of the new interpolation method.

Keywords

Main Subjects

[1] C.de Boor, A Practical Guide to Spline Interpolation, Springer-Verlag, New York, 1978.

[2] A.R. Haghighi and M. Roohi, The fractional cubic spline interpolation without using the derivative values, Indian Journal of Science and Technology, 5 (2012), pp. 3433-3439.

[3] H. Behforooz, Approximation by integro cubic splines, Appl. Math. Comput., 175 (2006), pp. 8-15.

[4] H. Behforooz, Interpolation by integro quintic splines Appl. Math. Comput., 216 (2010), pp. 364-367.

[5] F.G. Lang, X.P, On integro quartic spline interpolation, Appl. Math. Comput., 236 (2012), pp. 4214-4226.

[6] T. Wu and X.Zhang, Integro sextic spline interpolation and its super convergence, Appl. Math. Comput., 219 (2013), pp. 6431-6436.

[7] R.H. Wang, Numerical Approximation, Higher Education Press,  Higher Education Press, Beijing, 1999.

[8] L. Schumaker, Spline Functions: Basic Theory, Cambridge University Press, Cambridge, 2007.