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- Title
Several conservative compact schemes for a class of nonlinear Schrödinger equations with wave operator.
- Authors
Cheng, Xiujun; Wu, Fengyan
- Abstract
In this paper, several different conserving compact finite difference schemes are developed for solving a class of nonlinear Schrödinger equations with wave operator. It is proved that the numerical solutions are bounded and the numerical methods can achieve a convergence rate of O(τ2+h4)<inline-graphic></inline-graphic> in the maximum norm. Moreover, by applying Richardson extrapolation, the proposed methods have a convergence rate of O(τ4+h4)<inline-graphic></inline-graphic> in the maximum norm. Finally, several numerical experiments are presented to illustrate the theoretical results.
- Subjects
SCHRODINGER equation; FINITE differences; COMPUTATIONAL fluid dynamics; RICHARDSON extrapolation; FINITE difference method
- Publication
Boundary Value Problems, 2018, Vol 2018, Issue 1, p1
- ISSN
1687-2762
- Publication type
Article
- DOI
10.1186/s13661-018-0956-4