caa a22 4500 378884158 CHVBK 20180305123439.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0002 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0002 Numerical Stability Analysis of Solutions of PDEs [Elektronische Daten] 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 stimulated 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. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. finite dfference scheme nationallicence stability nationallicence nonlinear Shrödinger equation nationallicence discrete conservation nationallicence Čiegis Raimondas Vilnius Gediminas Technical University, Sailetekio al. 11, LT-10223 Vilnius, Lithuania. Čiegis Remigijus Vilnius Gediminas Technical University, Faculty of Humanities Muitines 8, LT-3000, Kaunas, Lithuania Computational Methods in Applied Mathematics De Gruyter 4/1(2004), 23-33 1609-4840 4:1<23 2004 4 cmam https://doi.org/10.2478/cmam-2004-0002 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0002 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Čiegis Raimondas Vilnius Gediminas Technical University, Sailetekio al. 11, LT-10223 Vilnius, Lithuania NATIONALLICENCE 700 1- Čiegis Remigijus Vilnius Gediminas Technical University, Faculty of Humanities Muitines 8, LT-3000, Kaunas, Lithuania NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/1(2004), 23-33 1609-4840 4:1<23 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter