期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 100, 期 -, 页码 74-82出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2021.08.026
关键词
Nonlinear Schrodinger equation with wave operator; Scalar auxiliary variable approach; Energy-conserving schemes; Convergence
资金
- National Natural Science Foundation of China [11901527]
- China Postdoctoral Science Foundation [2020M671087]
- Excellent Post-doctoral Innovative Talents Project of Hunan [2020RC2039]
- Science Foundation of Zhejiang Sci-Tech University [19062116-Y]
The numerical computation for the two-dimensional generalized nonlinear Schrodinger equations with wave operator is considered in this work. A three-level scheme for the equivalent system is proposed which conserves energy and is linearly implicit. The energy-conserving property, boundedness of the numerical solution and convergence analysis are derived, with numerical experiments confirming the theoretical results.
In this work, we consider the numerical computation for the two-dimensional generalized nonlinear Schrodinger equations with wave operator. Based on the scalar auxiliary variable (SAV) approach, the original problem is transformed into an equivalent one, which corresponds to the energy-conservation laws. We present an energy-conserving and linearly implicit three-level scheme for the equivalent system. The energy-conserving property, boundedness of the numerical solution and convergence analysis in the discrete maximum norm are derived, which has not restricted to specific forms of cubic nonlinear term f and not needed the sharply restriction on mesh size. Finally, numerical experiments on several models confirm our theoretical results.
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