Numerical Stability Analysis of Solutions of PDEs
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| 024 | 7 | 0 | |a 10.2478/cmam-2004-0002 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0002 | ||
| 245 | 0 | 0 | |a Numerical Stability Analysis of Solutions of PDEs |h [Elektronische Daten] |
| 520 | 3 | |a 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. | |
| 540 | |a 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. | ||
| 690 | 7 | |a finite dfference scheme |2 nationallicence | |
| 690 | 7 | |a stability |2 nationallicence | |
| 690 | 7 | |a nonlinear Shrödinger equation |2 nationallicence | |
| 690 | 7 | |a discrete conservation |2 nationallicence | |
| 700 | 1 | |a Čiegis |D Raimondas |u Vilnius Gediminas Technical University, Sailetekio al. 11, LT-10223 Vilnius, Lithuania. | |
| 700 | 1 | |a Čiegis |D Remigijus |u Vilnius Gediminas Technical University, Faculty of Humanities Muitines 8, LT-3000, Kaunas, Lithuania | |
| 773 | 0 | |t Computational Methods in Applied Mathematics |d De Gruyter |g 4/1(2004), 23-33 |x 1609-4840 |q 4:1<23 |1 2004 |2 4 |o cmam | |
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| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.2478/cmam-2004-0002 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Čiegis |D Raimondas |u Vilnius Gediminas Technical University, Sailetekio al. 11, LT-10223 Vilnius, Lithuania | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Čiegis |D Remigijus |u Vilnius Gediminas Technical University, Faculty of Humanities Muitines 8, LT-3000, Kaunas, Lithuania | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Computational Methods in Applied Mathematics |d De Gruyter |g 4/1(2004), 23-33 |x 1609-4840 |q 4:1<23 |1 2004 |2 4 |o cmam | ||
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| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||