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Numerical solution of the Maxwell equations in time-varying media using Magnus expansion

100%
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.
2
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Richardson Extrapolation combined with the sequential splitting procedure and the θ-method

100%
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.
3
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Generalizations and error analysis of the iterative operator splitting method

84%
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.
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