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Dieter Britz

Numerical stability of the Saul'yev finite difference algorithms for electrochemical kinetic simulations: Matrix stability analysis for an example problem involving mixed boundary conditions

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  • Department of Computer Science
  • Department of Chemistry
The stepwise numerical stability of the Saul'yev finite difference discretization of an example diffusional initial boundary value problem from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention has been paid to the effect of the discretization of the mixed, linear boundary condition on stability, assuming the two-point, forward-difference approximation for the gradient at the left boundary (electrode). Criteria regulating the error growth in time have been identified. In particular it has been shown that, in contrast to the claims of unconditional stability of the Saul'yev algorithms, reported in the literature, the left-right variant of the Saul'yev algorithm becomes unstable for large values of the dimensionless diffusion parameter λ = δt/h2, under mixed boundary conditions. This limitation is not, however, severe for most practical applications.
Original languageEnglish
JournalComputers and Chemistry
Volume19
Issue4
Pages (from-to)357-370
Number of pages14
ISSN0097-8485
DOIs
Publication statusPublished - 1995

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