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Construction and Convergence Analysis of Polynomial Spline Function of Degree Eight for Fractional Differential Equations

 Amina H. Ali*1, Faraidun K. Hamasalh1 and  Balen D. Yasin1

1Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq.

*Corresponding author’s e-mail: [email protected] 

Original: 7 March 2020        Revised: 13 September 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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In the present work, a special spline interpolation of the eighth degree has been constructed, and then theorem of existence and error bounded for this polynomial has been proved. Convergence analysis of the eight-degree spline polynomial has been shown. Later we have shown that this method is a numerical way to achieve solution for fractional differential equations. In addition, the proficiency and competency of this method are illustrated by given numerical examples

Key Words: Spline function, Convergence Analysis, Error bounded, Fractional Differential Equations