| Title |
Initial boundary-value problems for derivative nonlinear Schrödinger equation. Justification of two-step algorithm / |
| Translation of Title |
Pradinis-kraštinis uždavinys netiesinei išvestinių atžvilgiu Šriodingerio lygčiai. Dviejų žingsnių algoritmo pagrindimas. |
| Authors |
Meškauskas, Tadas ; Ivanauskas, Feliksas |
| DOI |
10.15388/NA.2002.7.2.15195 |
| Full Text |
|
| Is Part of |
Nonlinear analysis: modelling and control. 2002, vol. 7, no. 2, p. 69-104, 140.. ISSN 1392-5113 |
| Keywords [eng] |
derivative nonlinear Schrödinger equation ; initial boundary-value problem ; Bäcklund transformations ; Crank–Nicolson finite difference scheme ; convergence of difference schemes ; stability of difference schemes |
| Abstract [eng] |
We investigate two different initial boundary-value problems for derivative nonlinear Schrödinger equation. The boundary conditions are Dirichlet or generalized periodic ones. We propose a two-step algorithm for numerical solving of this problem. The method consists of Bäcklund type transformations and difference scheme. We prove the convergence and stability in C and H^1 norms of Crank–Nicolson finite difference scheme for the transformed problem. There are no restrictions between space and time grid steps. For the derivative nonlinear Schrödinger equation, the proposed numerical algorithm converges and is stable in C^1 norm. |
| Type |
Journal article |
| Language |
English |
| Publication date |
2002 |
| CC license |
|
