A reliable automatic simulation of singular electroanalytical transients, by the adaptive Huber method for Volterra integral equations
Authors:
- L. K. Bieniasz
Abstract
In a number of transient electroanalytical experiments (such as, in particular, the potential step chronoamperometry) one expects current-time responses having a singularity at time t =0. A reliable simulation of such singular responses is a di ffi cult task. Conventional simulation techniques fail to provide accurate results close to the singularity. A recent extension [L. K. Bieniasz, J. Comput. Appl. Math. 323 (2017) 136] of the adaptive Huber method for solving Volterra integral equations (IEs) is shown to overcome this di ffi culty in cases when the current behaves like t − 1/2 for t → 0. The method requires an availability of highly accurate approximants for computing certain integrals of the kernel functions occurring in the IEs. Relevant approximants are elaborated for several most important kernel functions speci fi c of one-dimensional di ff usion, and one kernel function for two-dimensional di ff usion. The resulting algorithm is tested on two examples of single IEs describing chronoamperometry and cyclic voltammetry for a single reversible charge transfer, and one example of an IE system describing chronoamperometry for an E rev E rev mechanism. Singular transients are simulated automatically with a prescribed accuracy, even for t arbitrarily close to the singularity.
- Record ID
- CUT4ceb662bea4e4a0fb75a572510cccaa2
- Publication categories
- ;
- Author
- Journal series
- Journal of Electroanalytical Chemistry, ISSN 1572-6657, e-ISSN 1873-2569
- Issue year
- 2017
- Vol
- 799
- Pages
- 40-52
- Other elements of collation
- wykr.; Bibliografia (na s.) - 51-52; Bibliografia (liczba pozycji) - 67; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 799
- Keywords in English
- volterra integral equations, weakly singular kernels, weakly singular solutions, adaptive methods, product-integration, computational electrochemistry
- DOI
- DOI:10.1016/j.jelechem.2017.05.027 Opening in a new tab
- URL
- http://www.sciencedirect.com/science/article/pii/S1572665717303880 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/CUT4ceb662bea4e4a0fb75a572510cccaa2/
- URN
urn:pkr-prod:CUT4ceb662bea4e4a0fb75a572510cccaa2
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