期刊
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
卷 20, 期 3, 页码 517-530出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/cmam-2019-0111
关键词
Regularized Collocation; Weighted Norms; Electrochemical Impedance Spectroscopy; Distribution of Diffusion Times
资金
- AMMODIT-consortium
- JESH-programme
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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