This article is cited in 7 papers

Integro-differential equations and functional analysis

Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind

Aleksandr N. Tynda^a, Samad Noeiaghdam^bc, Denis N. Sidorov<sup>bde

a</sup> Penza State University, Penza, Russian Federation
^b Irkutsk National Research Technical University, Irkutsk, Russian Federation
^c South Ural State University, Chelyabinsk, Russian Federation
^d Energy Systems Institute SB RAS, Irkutsk, Russian Federation
^e Irkutsk State University, Irkutsk, Russian Federation

Abstract: {Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind} {Polynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind} The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gauss-type 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 Contrôle 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.

Keywords: integral equation, discontinuous kernel, spline collocation method, convergence, CESTAC method, CADNA library.

UDC: 519.642.5

MSC: 45H05, 65R20

Received: 25.12.2021
Revised: 17.01.2022
Accepted: 21.02.2022

Language: English

DOI: 10.26516/1997-7670.2022.39.62

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