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fitzhugh–nagumo equations

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Error estimates for a FitzHugh–Nagumo parameter-dependentreaction-diffusion system
Konstantinos Chrysafinos, Sotirios P. Filopoulos, Theodosios K. Papathanasiou
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 1 / January 2013

Published online by Cambridge University Press:

23 November 2012, pp. 281-304

Print publication:

January 2013
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Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolicPDEs are examined. The schemes under consideration are discontinuous in time butconforming in space and of arbitrary order. Stability estimates are presented in thenatural energy norms and at arbitrary times, under minimal regularity assumptions.Space-time error estimates of arbitrary order are derived, provided that the naturalparabolic regularity is present. Various physical parameters appearing in the model aretracked and numerical examples are presented.