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Extension of the Adaptive Huber Method for Solving Integral Equations Occurring in Electroanalysis, onto Kernel Function Representing Fractional Diffusion
Author(s) -
Bieniasz Lesław K.
Publication year - 2011
Publication title -
electroanalysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.574
H-Index - 128
eISSN - 1521-4109
pISSN - 1040-0397
DOI - 10.1002/elan.201100026
Subject(s) - kernel (algebra) , integral equation , integral transform , diffusion , mathematics , diffusion equation , fractional calculus , transformation (genetics) , formalism (music) , extension (predicate logic) , mathematical analysis , physics , computer science , chemistry , thermodynamics , pure mathematics , biochemistry , economy , gene , economics , programming language , service (business) , art , musical , visual arts
Electroanalytical transient experiments performed under conditions of anomalous diffusion have recently attracted some attention. In order to enable automatic simulation of such experiments in the framework of the formalism of integral equations, the adaptive Huber method, recently elaborated by the present author, is extended onto integral transformation kernel function K ( t , τ )=( t − τ ) α /2−1 (where 0< α ≤1), representing fractional diffusion. The extended method is tested on a model integral equation describing cyclic voltammetry for a reversible charge transfer reaction. The performance of the method is found similar to the case of ordinary diffusion.