Open AccessPolynomial Spline Collocation Method for Solving Weakly Regular Volterra Integral Equations of the First Kind
Author(s) -
Aleksandr Tynda,
Samad Noeiaghdam,
Denis Sidorov
Publication year - 2022
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2022.39.62
Subject(s) - mathematics , collocation method , piecewise , volterra integral equation , discretization , quadrature (astronomy) , polynomial , spline (mechanical) , collocation (remote sensing) , gaussian quadrature , projection (relational algebra) , integral equation , mathematical analysis , nyström method , algorithm , computer science , differential equation , ordinary differential equation , engineering , structural engineering , machine learning , electrical engineering
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.