Damping of Crank–Nicolson error oscillations

Britz, Dieter; Østerby, Ole; Strutwolf, Jörg

doi:10.1016/s0097-8485(02)00075-x

Cited by 57 publications

(44 citation statements)

References 46 publications

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“…In [2] three of the methods (IM, Pearson, EI) have been applied to two problems from electrochemistry where the discontinuity appears between the initial condition and one boundary condition. Here we shall compare the methods on a problem with a jump discontinuity in the initial condition.…”

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confidence: 99%

Five Ways of Reducing the Crank-Nicolson Oscillations

Østerby¹

2002

DPB

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Five Ways of Reducing the Crank-Nicolson Oscillations

Østerby¹

2002

DPB

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“…Typically, M was chosen at about 400, which resulted in an expansion factor 1 of no more than about 1.1. It has been established [43] that a value no more than 1.2 is optimal.…”

Section: Discretisation Simulation Methodsmentioning

confidence: 99%

Several ways to simulate time dependent liquid junction potentials by finite differences

Britz

Strutwolf

2014

Electrochimica Acta

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a b s t r a c tSeveral ways of simulating time-dependent migration effects at an electrolytic liquid junction are explored, for a simple uni-univalent electrolyte, both with the full Nernst-Planck-Poisson (NPP) equation set and the reduced set from the electroneutrality condition (ENC) assumption. Using the NPP approach, the system can be simulated using all three variables (method AB), the two concentrations and the potential, or the two concentrations and the potential field (method ABE), or in principle by substituting for the potential field, thereby reducing to the two concentration variables (method AB). The two first methods are about equally efficient, whereas the latter method is seen to be quite inaccurate. Results at long times compare very well with the Henderson equation. Using the full NPP set, junction potentials are time-dependent but not when applying the ENC, where the potential rises to the Henderson value immediately. Results for KCl and HCl are presented, with left/right concentration ratios equal to 0.1 in both cases.

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“…This is not an instability due to an error propagation as one might get using an unstable simulation method; this is shown by the points on two of the curves, obtained by the eigenvalue-eigenvector method, which computes a current directly for each T value, without stepping with time intervals. This is the reason that the word "waves" is used here, rather than "oscillation", such as one obtains with the Crank-Nicolson method [79] applied to problems with an initial transient [80,81], which are indeed oscillatory error propagation effects. We have no explanation for this puzzling effect, which is clearly a property of the transformed grid.…”

Section: Verbrugge-baker Transformation Vbmentioning

confidence: 99%

Minimum grid digital simulation of chronoamperometry at a disk electrode

Britz

Østerby

Strutwolf

2012

Electrochimica Acta

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a b s t r a c tWe seek to find the best ways to achieve a minimum grid with a given target accuracy in the computed current in the simulation of a diffusion limited chronoamperometric experiment at an ultramicrodisk electrode. We present some results for direct discretisation on the cylindrical geometry in (R, Z) space and in transformed coordinates (Â, ), comparing four commonly used transformations. In all cases, the use of multi-point spatial derivative approximations are explored to find an optimum. Orthogonal collocation is studied in the two dimensions, and found less efficient than an evenly divided grid and smaller multi-point approximations. The eigenvalue-eigenvector method is studied and found to be relatively inefficient but was useful in providing some information on error waves seen with three of the four transformations used. These error waves are not due to an error propagation, a fact that became clear from the eigenvalue-eigenvector method, which reproduced the waves.

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Damping of Crank–Nicolson error oscillations

Cited by 57 publications

References 46 publications

Five Ways of Reducing the Crank-Nicolson Oscillations

Five Ways of Reducing the Crank-Nicolson Oscillations

Several ways to simulate time dependent liquid junction potentials by finite differences

Minimum grid digital simulation of chronoamperometry at a disk electrode

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