COMPARISON OF INTEGRO QUADRATIC AND QUARTIC SPLINE INTERPOLATION

Yıl 2020, Cilt: 10 Sayı: 1, 150 - 160, 01.01.2020

A. R. Haghighi A. Aghazedeh A. Abedini

Öz

In this paper quadratic and quartic B-splines were used for reconstruction of an approximating function, where the integral values of successive subintervals were used instead of function values at the knots. After introducing integro quadratic and quartic interpolation a comparison was done between them through presenting numerical examples. The interpolation errors for quadratic and quartic integro interpolation are studied. Numerical results illustrate the eciency and eectiveness of the new interpolation methods.

Anahtar Kelimeler

Integral values, quadratic and quartic B-spline, integro interpolation, super convergence, error analysis.

Kaynakça

• Haghighi, A., and Pakrou, Sh., (2016) Comparison of the LBM with the modified local Crank-Nicolson method solution of transient one-dimensional nonlinear Burgers’ equation. International Journal of Computing Science and Mathematics 7.5: 459-466.
• Haghighi, A. R., and Shahbazi Asl, M., (2014), A comparison between alternating segment Crank- Nicolson and explicit-implicit schemes for the dispersive equation. International Journal of Computing Science and Mathematics, 5(4), 405-417.
• Haghighi, A. R., Ghejlo, H. H., and Asghari, N., (2013), Explicit and implicit methods for fractional diffusion equations with the riesz fractional derivative. Indian Journal of Science and Technology, 6(7), 4881-4885.
• Haghighi, A. R. and Roohi, M. (2012), The fractional cubic spline interpolation without using the derivative values, Indian Journal of Science and Technology 5.10: 3433-3439.
• Behforooz, H., (2006), Approximation by integro cubic splines, Applied mathematics and computation, 175(1), pp.8-15.
• Behforooz, H., (2010), Interpolation by integro quintic splines, Applied Mathematics and Computa- tion, 216(2), pp.364-367.
• Zhanlav, T. and Mijiddorj, R., (2010), The local integro cubic splines and their approximation prop- erties, Appl. Math. Comput. 216, 22152219.
• Ahmadi Shali, J., Haghighi, A. R., Asghary, N., and Soleymani, E., (2017), Convergence of Integro Quartic and Sextic B-Spline interpolation. Sahand Communications in Mathematical Analysis.
• De Boor, C., (1978), A Practical Guide to Splines, Springer-Verlag, New York.
• Wang, R.H., (1999), Numerical Approximation, Higher Education Press, Beijing.
• Schumaker, L., (2007), Spline Functions: Basic Theory. Cambridge University Press.
• Lang, F.G. and Xu, X.P., (2012), On integro quartic spline interpolation, Journal of Computational and Applied Mathematics, 236(17), pp.4214-4226.