ESTIMATES OF ERROR BOUNDS FOR SEVENTIC SPLINE POLYNOMIAL
Author(s):
Karwan Hama Faraj Jwamer1, Faraidun Kadir Hamasalh2, Ridha Ghafoor Kareem Muhhamad3, Rando Rasul Qadir4
1 Professor, Department of Mathematics, University of Sulaimani, Iraq, Ph. +9647701428111, Fax: +9647701428111, Email: karwan.jwamer@univsul.edu.iq.
2 Assistant Professor Department of Mathematics, University of Sulaimani, Iraq, Ph. +9647701528274, Fax: +9647701528274, Email: faraidun.hamasalh@univsul.edu.iq.
3 Assistant Lecturer, Department of Mathematics, School of basic Education, University of Sulaimani, Iraq, Ph. +9647701105111, Fax: +9647701105111, Email: ridha.karem@univsul.edu.iq.
4 Lecturer, Department of Mathematics, School of basic Education, University of Sulaimani, Iraq, Ph. +9647502086654, Fax: +9647502086654, Email: randorasul@gmail.com.
Volume:
XIV
No.
2
Pages:
1 - 10
Date:
March 2017
Abstract:
A convergence analysis for a new model of spline polynomial has been presented in this paper to obtain an accurate estimation for the error bounds related to seventic spline interpolation. The results matched closely with the values of a given function at the knots of a selected partition of the interval (0, 1). These also agreed with the values of the first derivative at the boundary points. The spline approximation was found to be of higher accuracy. In addition, the existence and uniqueness for the class of spline function of degree seven has been discussed and verified. The results were verified with the help of two examples of boundary value problems and comparisons with analytical solutions were made at different step sizes.