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Generalizations and error analysis of the iterative operator splitting method

100%
Ladics T., Faragó I.
Open Mathematics
|
2013
|
tom 11
|
nr 8
1416-1428
EN
The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to the order of accuracy.
2
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An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model

81%
Faragó I., Izsák F., Szabó T., Kriston Á.
Open Mathematics
|
2013
|
tom 11
|
nr 4
746-759
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.
3
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Numerical solution of the Maxwell equations in time-varying media using Magnus expansion

81%
Faragó I., Havasi Á., Horváth R.
Open Mathematics
|
2012
|
tom 10
|
nr 1
137-149
EN
For the Maxwell equations in time-dependent media only finite difference schemes with time-dependent conductivity are known. In this paper we present a numerical scheme based on the Magnus expansion and operator splitting that can handle time-dependent permeability and permittivity too. We demonstrate our results with numerical tests.
4
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Richardson Extrapolation combined with the sequential splitting procedure and the θ-method

81%
Zlatev Z., Faragó I., Havasi Á.
Open Mathematics
|
2012
|
tom 10
|
nr 1
159-172
EN
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
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