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

作     者：Tynda, Aleksandr Noeiaghdam, Samad Sidorov, Denis 

作者机构：Higher and Applied Mathematics Department Penza State University Penza440026 Russia Industrial Mathematics Laboratory Baikal School of BRICS Irkutsk National Research Technical University Irkutsk664074 Russia Department of Applied Mathematics and Programming South Ural State University Lenin prospect 76 Chelyabinsk454080 Russia Energy Systems Institute Siberian Branch of Russian Academy of Science Irkutsk664033 Russia Institute of Mathematics and Information Technologies Irkutsk State University Irkutsk664025 Russia 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2021年

核心收录：

主　　题：Integral equations 

摘      要：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 *** Codes 45H05, 65R20 © 2021, CC BY.