Paper title:

Numerical Solution of Volterra Integral Equations with a Weakly Singular Kernel Using the Seventh Order Non-Polynomial Spline Function Method

Published in: Issue 1, (Vol. 16) / 2022
Publishing date: 2022-04-05
Pages: 24-29
Author(s): HASAN Arkan Sh., MOHAMMED Sizar A.
Abstract. In this paper, the seventh-order non-polynomial slice function (NPSF7) was used to solve the Volterra integrative equation of the second type with a weakly single kernel. New problems were applied to demonstrate the effectiveness and accuracy of our method. And also the comparison we have made between the results calculated by our method and the results obtained by other methods like NPSF1 and NPSF6 is provided in order to validate this method
Keywords: Volterra Integral Equation, Weakly Singular Kernel, Non-polynomial Spline Functions

1. Hermann Brunner, ''Non-polynomial Spline Collocation for Volterra Equation with Weakly Singular Kernels''; SIAM J-Numer. Anal, 20(6), 1106-1119, 1982.

2. Baruch Cahlon and Louis J. Nachman,"Numerical Solution of Volterra Integral Equations with a solution Dependent Delay''; Journal of Mathematical Analysis and Applications, 112,541-562, 1985.

3. Baruch Cahlon, "On the Numerical Stability of Volterra Integral Equations with Delay Argument"; Journal of Computational and Applied Mathematics, 33,97-104, 1990.

4. George Karakostas, I.P.Stavroulakis and Yumiwn, "Oscillations of Volterra Integral Equation with Delay "; Tohoka. Math.J.583-605, 1993.

5. Vilmos Horvat,"On Collocation Methods for Volterra Integral Equations with Delay Arguments'', Mathematical communications, 4, 93-109, 1999.

6. Daniel Franco and O’Regan, "Solution of Volterra integral equations with infinite Delay ", 2005.

7. Muna M. Mustafa and Thekra A. Latiff Ibrahem, "Numerical solution of Volterra Integral Equations with Delay Using Block Methods ", AL-Fatih ournal.No.36, 2008.

8. shtiaq Ali, Hermann Brunner and Tao Tang," Spectral Methods for Pantograph-Type Differential and Integral Equation with Multiple Delays"; Front. Math. China, 4(1), 49–61, 2009.

9. M. Avaji, J.S. Hafshejani,S.S.Dehchesmeh and D.F. Ghahfarokhi;" Solution of Delay Volterra Integral Equation Using the Variation Iteration Method''; Journal of Applied Sciences,12(2), 196-200,2012.

10. Joser Morales and Edixon M.Rojas; "Hyers-Ulam and Hyers-Ulam Rasstas Stability of Nonlinear Integral Equation with Delay"; Int. J. Nonlinear Anal. Appl. 2 (2011) No.2, 1-6, 2011.

11. Muna M. Mustafa and Sarah H. Harbi;''Solution of Second Kind Volterra Integral Equations Using Non-Polynomial Spline Function"; Baghdad Science Journal, Vol.11, No.2, 2014.

12. Sarah H. Harbi, Mohammed A. Murad, Saba N. Majeed; "A Solution of Second Kind Volterra Integral Equations Using Third Order Non-Polynomial Spline Function "; Baghdad Science Journal, Vol.12, No.2, 2015.

13. Parviz Darania "Multistep Collocation Method for Non-linear Delay Integral Equation'' (SCMA), Vol.3, No.2, 47-65, 2016.

14. Sarah H. Harbi;'' Algorithms for Solving Volterra Integral Equations Using Non-Polynomial Spline Functions '' Thesis, University of Baghdad, 2013.

15. GENG, F and SHEN, F 2010- Solving Integral Equation with Weakly Singular kernel in the Reproducing kernel Space. Islamic Azad University Karaj Branch, vol.4.2, pp.159-170.

16. IBRAHIM, E. A. E., Gadir Abdel, A. R. A. R. A., Rahman, Z. A. M. A. A., & Hassan, R. H. I. (2021). Analytical and Numerical Solutions of Linear Volterra Integral Equations of the Second Kind with Weakly Singular Kernel by using the Sixth Order of Non-polynomial Spline Functions by Matlab. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(14), 2435-2448.

Back to the journal content
Creative Commons License
This article is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
Home | Editorial Board | Author info | Archive | Contact
Copyright JACSM 2007-2022