Numerical Stability Analysis of Solutions of PDEs

Raimondas Čiegis, Remigijus Čiegis
2004 Computational Methods in Applied Mathematics  
In this paper we investigate two iterative methods for solving one problem of nonlinear optics. The main goal is not only to find a stationary solution but also to investigate its stability. It is shown that both methods have very different stability properties and the less stable algorithm is close to the approximation of the physically important non-stationary problem. We also propose a new iterative algorithm for solving a more complicated problem which describes the optical conjugation in
more » ... imulated Brillouin backscattering with pump depletion. This algorithm is based on a symmetrical splitting scheme and the nonlinear interaction is approximated by using the special mass conservation property of the discrete problem. Thus, we obtain a conservative iterative algorithm. The results of the numerical experiments are presented and they confirm our theoretical conclusions. 2000 Mathematics Subject Classification: 65N20; 65M25.
doi:10.2478/cmam-2004-0002 fatcat:f36xm2b3ovh2nopn4lt7vzrlou