A numerical algorithm for simulation of the Q-switched fiber laser using the travelling wave model |
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Authors: | R. Čiegis A. Dement’ev I. Laukaitytė |
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Affiliation: | (1) Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania;(2) Institute of Physics, Goštauto 12, LT-2600 Vilnius, Lithuania |
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Abstract: | We develop a finite-difference scheme for approximation of a system of nonlinear PDEs describing the Q-switching process. We construct it by using staggered grids. The transport equations are approximated along characteristics, and quadratic nonlinear functions are linearized using a special selection of staggered grids. The stability analysis proves that a connection between time and space steps arises only due to approximation requirements in order to follow exactly the directions of characteristics. The convergence analysis of this scheme is done in two steps. First, some estimates of the uniform boundedness of the discrete solution are proved. This part of the analysis is done locally, in some neighborhood of the exact solution. Second, on the basis of the obtained estimates, the main stability inequality is proved. The second-order convergence rate with respect to the space and time coordinates follows from this stability estimate. Using the obtained convergence result, we prove that the local stability analysis in the selected neighborhood of the exact solution is sufficient. |
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Keywords: | Q-switch nonlinear problems numerical algorithms convergence analysis staggered grids |
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