An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model

István Faragó; Ferenc Izsák; Tamás Szabó; Ákos Kriston

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 746-759
  • ISSN: 2391-5455

Abstract

top
An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.

How to cite

top

István Faragó, et al. "An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model." Open Mathematics 11.4 (2013): 746-759. <http://eudml.org/doc/269280>.

@article{IstvánFaragó2013,
abstract = {An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.},
author = {István Faragó, Ferenc Izsák, Tamás Szabó, Ákos Kriston},
journal = {Open Mathematics},
keywords = {Reaction-diffusion equation; Finite difference method; IMEX method; Staggered grid; reaction-diffusion equation; finite difference method; staggered grid; implicit-explicit method; convergence; proton exchange membrane fuel cell},
language = {eng},
number = {4},
pages = {746-759},
title = {An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model},
url = {http://eudml.org/doc/269280},
volume = {11},
year = {2013},
}

TY - JOUR
AU - István Faragó
AU - Ferenc Izsák
AU - Tamás Szabó
AU - Ákos Kriston
TI - An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 746
EP - 759
AB - An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.
LA - eng
KW - Reaction-diffusion equation; Finite difference method; IMEX method; Staggered grid; reaction-diffusion equation; finite difference method; staggered grid; implicit-explicit method; convergence; proton exchange membrane fuel cell
UR - http://eudml.org/doc/269280
ER -

References

top
  1. [1] Ascher U.M., Ruuth S.J., Spiteri R.J., Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math., 1997, 25(2–3), 151–167 http://dx.doi.org/10.1016/S0168-9274(97)00056-1 Zbl0896.65061
  2. [2] Ascher U.M., Ruuth S.J., Wetton B.T.R., Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 1995, 32(3), 797–823 http://dx.doi.org/10.1137/0732037 Zbl0841.65081
  3. [3] Burrage K., Hundsdorfer W.H., Verwer J.G., A study of B-convergence of Runge-Kutta methods, Computing, 1986, 36(1–2), 17–34 http://dx.doi.org/10.1007/BF02238189 Zbl0572.65053
  4. [4] Deuflhard P., Recent progress in extrapolation methods for ordinary differential equations, SIAM Rev., 1985, 27(4), 505–535 http://dx.doi.org/10.1137/1027140 Zbl0602.65047
  5. [5] Faragó I., Havasi Á., Zlatev Z., Richardson-extrapolated sequential splitting and its application, J. Comput. Appl. Math., 2009, 226(2), 218–227 http://dx.doi.org/10.1016/j.cam.2008.08.003 Zbl1160.65022
  6. [6] Frank J., Hundsdorfer W., Verwer J.G., On the stability of implicit-explicit linear multistep methods, Special Issue on Time Integration, Amsterdam, 1996, Appl. Numer. Math., 1997, 25(2–3), 193–205 http://dx.doi.org/10.1016/S0168-9274(97)00059-7 
  7. [7] Hoff D., Stability and convergence of finite difference methods for systems of nonlinear reaction-diffusion equations, SIAM J. Numer. Anal., 1978, 15(6), 1161–1177 http://dx.doi.org/10.1137/0715077 Zbl0411.76062
  8. [8] Hundsdorfer W., Verwer J., Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Ser. Comput. Math., 33, Springer, Berlin, 2003 Zbl1030.65100
  9. [9] Koto T., IMEX Runge-Kutta schemes for reaction-diffusion equations, J. Comput. Appl. Math., 2008, 215(1), 182–195 http://dx.doi.org/10.1016/j.cam.2007.04.003 Zbl1141.65072
  10. [10] Kriston Á., Inzelt G., Faragó I., Szabó T., Simulation of the transient behavior of fuel cells by using operator splitting techniques for real-time applications, Computers & Chemical Engineering, 2010, 34(3), 339–348 http://dx.doi.org/10.1016/j.compchemeng.2009.11.006 
  11. [11] Litster S., Djilali N., Mathematical modelling of ambient air-breathing fuel cells for portable devices, Electrochimica Acta, 2007, 52(11), 3849–3862 http://dx.doi.org/10.1016/j.electacta.2006.11.002 
  12. [12] Newman J., Thomas-Alyea K.E., Electrochemical Systems, 3rd ed., The Electrochemical Society Series, John Wiley & Sons, Hoboken, 2004 
  13. [13] Robinson M., IMEX method convergence for a parabolic equation, J. Differential Equations, 2007, 241(2), 225–236 http://dx.doi.org/10.1016/j.jde.2007.07.001 Zbl1125.35004
  14. [14] Subramanian V.R., Boovaragavan V., Diwakar V.D., Toward real-time simulation of physics based Lithium-ion battery models, Electrochemical and Solid-State Letters, 2007, 10(11), A255–A260 http://dx.doi.org/10.1149/1.2776128 
  15. [15] Verwer J.G., Convergence and order reduction of diagonally implicit Runge-Kutta schemes in the method of lines, In: Numerical Analysis, Dundee, 1985, Pitman Res. Notes Math. Ser., 140, Longman Sci. Tech., Harlow, 1985, 220–237 
  16. [16] Verwer J.G., Blom J.G., Hundsdorfer W., An implicit-explicit approach for atmospheric transport-chemistry problems, Appl. Numer. Math., 1996, 20(1–2), 191–209 http://dx.doi.org/10.1016/0168-9274(95)00126-3 Zbl0853.76092
  17. [17] Ziegler C., Yu H.M., Schumacher J.O., Two-phase dynamic modeling of PEMFCs and simulation of cyclovoltammograms, Journal of the Electrochemical Society, 2005, 152(8), A1555–A1567 http://dx.doi.org/10.1149/1.1946408 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.