An adaptive Huber method for nonlinear systems of Volterra integral equations with weakly singular kernels and solutions
Authors:
- L. K. Bieniasz
Abstract
Numerical methods for solving nonlinear systems of weakly singular Volterra integral equations (VIEs) possessing weakly singular solutions appear almost nonexistent in the literature,exceptforafewtreatmentsofsinglefirstkindAbelequations.Toreducethisgap, anextensionispresented,of theadaptiveHubermethoddesignedforVIEswithsingular kernels such as K ( t ,τ) = ( t − τ) − 1 / 2 and K ( t ,τ) = exp [− λ( t − τ) ] ( t − τ) − 1 / 2 (where λ ≥ 0) and a variety of nonsingular kernels. The method was thus far restricted to bounded solutions having at least two derivatives. Under a number of assumptions specified, the extension applies to solutions U μ ( t ) that can be written as sums of singularcomponents c μ t − 1 / 2 (withunknowncoefficients c μ ),andnonsingularcomponents U μ ( t ) . In the solution process, factor t − 1 / 2 is handled analytically, whereas c μ and U μ ( t ) are determined numerically. Computational experiments reveal that the extended methoddeterminessingularsolutionsequallywellastheunextendedmethoddetermined nonsingularsolutions.ThemethodisintendedprimarilyforaclassofVIEsencounteredin electroanalyticalchemistry,butitcanalsobeofinteresttootherapplicationareas.
- Record ID
- CUT97ee443fff5c4cdd91a7d851f96b96c1
- Publication categories
- ;
- Author
- Journal series
- Journal of Computational and Applied Mathematics, ISSN 0377-0427, e-ISSN 1879-1778
- Issue year
- 2017
- Vol
- 323
- Pages
- 136-146
- Other elements of collation
- tab.; wykr.; Bibliografia (na s.) - 146; Bibliografia (liczba pozycji) - 39; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 323
- Keywords in English
- volterra integral equations, weakly singular kernels, weakly singular solutions, adaptive methods, product-integration, computational electrochemistry
- DOI
- DOI:10.1016/j.cam.2017.04.018 Opening in a new tab
- URL
- http://www.sciencedirect.com/science/article/pii/S0377042717301887 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 35
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT97ee443fff5c4cdd91a7d851f96b96c1/
- URN
urn:pkr-prod:CUT97ee443fff5c4cdd91a7d851f96b96c1
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.