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Numerical analysis of nonlinear model of excited carrier decay

100%
Tumanova N., Čiegis R., Meilūnas M.
Open Mathematics
|
2013
|
tom 11
|
nr 6
1140-1152
EN
This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.
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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Opposing flows in a one dimensional convection-diffusion problem

84%
O’Riordan E.
Open Mathematics
|
2012
|
tom 10
|
nr 1
85-100
EN
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator to construct a parameter-uniform numerical method for this class of singularly perturbed problems.
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