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On continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition

Faragó, István; Korotov, Sergey; Szabó, Tamás — 2015

Application of Mathematics 2015

In this work, we present and discuss continuous and discrete maximum/minimum principles for reaction-diffusion problems with the Neumann boundary condition solved by the finite element and finite difference methods.

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

István Faragó; Ferenc Izsák; Tamás Szabó; Ákos Kriston — 2013

Open Mathematics

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.

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