Journal
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
Volume 20, Issue 3, Pages 517-530Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/cmam-2019-0111
Keywords
Regularized Collocation; Weighted Norms; Electrochemical Impedance Spectroscopy; Distribution of Diffusion Times
Categories
Funding
- AMMODIT-consortium
- JESH-programme
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This paper is inspired by recently proposed approach for interpreting data of Electrochemical Impedance Spectroscopy (EIS) in terms of Distribution of Diffusion Times (DDT). Such an interpretation requires to solve a Fredholm integral equation of the first kind, which may have a non-square-integrable kernel. We consider a class of equations with above-mentioned peculiarity and propose to regularize them in weighted functional spaces. One more issue associated with DDT-problem is that EIS data are available only for a finite number of frequencies. Therefore, a regularization should unavoidably be combined with a collocation. In this paper we analyze a regularized collocation in weighted spaces and propose a scheme for its numerical implementation. The performance of the proposed scheme is illustrated by numerical experiments with synthetic data mimicking EIS measurements.
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