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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2022. Vol 39

Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind

Author(s)
Aleksandr N. Tynda1, Samad Noeiaghdam2,3, Denis N. Sidorov4,2,5

1Penza State University, Penza, Russian Federation

2Irkutsk National Research Technical University, Irkutsk, Russian Federation

3South Ural State University, Chelyabinsk, Russian Federation

4Energy Systems Institute SB RAS, Irkutsk, Russian Federation

5Irkutsk State University, Irkutsk, Russian Federation, contact.dns@gmail.com

Abstract
The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gausstype quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation method.
About the Authors

Aleksandr N. Tynda, Cand. Sci. (Phys.–Math.), Assoc. Prof., Penza State University, Penza, 440026, Russian Federation, tyndaan@mail.ru

Samad Noeiaghdam, Dr. Sci. (PhD), Assoc. Prof., Irkutsk National Research Technical University, Irkutsk, 664074, Russian Federation; South Ural State University, Chelyabinsk, 454080, Russian Federation, noiagdams@susu.ru

Denis Sidorov, Dr. Sci. (Phys.–Math.), Prof., Energy Systems Institute SB RAS, Irkutsk, 664033, Russian Federation; Irkutsk National Research Technical University, Irkutsk, 664074, Russian Federation; Irkutsk State University, Irkutsk, 664003, Russian Federation, sidorovdn@istu.edu

For citation
Tynda A. N., Noeiaghdam S., Sidorov D. N. Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 39, pp. 62–79. https://doi.org/10.26516/1997-7670.2022.39.62
Keywords
integral equation, discontinuous kernel, spline collocation method, convergence, CESTAC method, CADNA library
UDC
519.642.5
MSC
45H05, 65R20
DOI
https://doi.org/10.26516/1997-7670.2022.39.62
References
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