Author:
Hamasalih Faraidun,Qadir Rahel
Abstract
In this article, the researchers develop a new type of spline function with fractional order which constructs two distinct formulas for the proposed method by using fractional boundary conditions and fractional continuity conditions. These methods are used to solve linear Volterra and Fredholm-integral equations of the second kind. The convergence analysis is studied. Moreover, some numerical examples are provided and compared to illustrate the efficiency and applicability of the proposed methods.
Publisher
Academia Romana Filiala Cluj
Reference15 articles.
1. K. Parand,A.A. Aghaei, M. Jani, A. Ghodsi, A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression. Math. Comput. Simulation, 180, (2021), pp. 114–128. https://doi.org/10.1016/j.matcom.2020.08.010
2. S.Hatamzadeh-Varmazyar, Z. Masouri, Numerical solution of second kind Volterra and Fredholm integral equations based on a direct method via triangular functions. Int.J. Ind. Math., 11(2), (2019), pp. 79–87.
3. K. Maleknejad, J. Rashidinia, H. Jalilian, Quintic Spline functions and Fredholm integral equation. Comput. Methods Differ. Equ., 9(1), (2021), pp. 211–224. https://doi.org/10.22034/CMDE.2019.31983.1492
4. F. Muller, W. Varnhorn, On approximation and numerical solution of Fredholm integral equations of second kind using quasi-interpolation. Appl. Math. Comput., 217(13)(2011), pp. 6409–6416, https://doi.org/10.1016/j.amc.2011.01.022
5. Panda, S.C.Martha, A. Chakrabarti, A modified approach to numerical solution of Fredholm integral equations of the second kind. Appl. Math. Comput., 271 (2015),pp. 102–112. https://doi.org10.1016/j.amc.2015.08.111