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

• Autorzy: István Faragó , Ferenc Izsák , Tamás Szabó , Ákos Kriston
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Reaction-diffusion equation; Finite difference method; IMEX method; Staggered grid

Kategorie tematyczne

• 65M06: Finite difference methods
• 65M20: Method of lines
• 65M12: Stability and convergence of numerical methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 4
• Strony: 746-759

Daty

wydano

2013-04-01

online

2013-01-29

Twórcy

autor

István Faragó

• Eötvös Loránd University

autor

Ferenc Izsák

• Eötvös Loránd University

autor

Tamás Szabó

• Basque Center for Applied Mathematics

autor

Ákos Kriston

• Eötvös Loránd University

Bibliografia

• [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
• [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
• [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
• [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
• [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
• [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] 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
• [8] Hundsdorfer W., Verwer J., Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Ser. Comput. Math., 33, Springer, Berlin, 2003
• [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
• [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] 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] Newman J., Thomas-Alyea K.E., Electrochemical Systems, 3rd ed., The Electrochemical Society Series, John Wiley & Sons, Hoboken, 2004
• [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
• [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] 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] 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
• [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

Identyfikatory

DOI

10.2478/s11533-012-0157-9