摘要
针对带有弱阻尼项的非线性Schrdinger方程周期初值问题,研究一个全离散Fourier拟谱格式。基于对拟谱逼近解所做的一系列的一致先验估计,得到拟谱格式在[0,T]上按L2模的稳定性和拟谱逼近解最优的误差估计。最后证明由全离散Fourier拟谱格式生成的离散动力系统存在整体的吸引子。
A fully discrete Fourier pseudo-spectral scheme to a nonlinear Schoedinger equation with weakly damped is analyzed. On the basis of a series of the time-uniform priori estimates of the pseudo-spectral approximate solutions, the stability of the fully discrete Fourier pseudo-spectral scheme and the error bounds of optimal order of the approximate solutions are obtained in L2-module over a finite time interval [ O, T]. Finally, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2010年第3期296-303,共8页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(10371077)
黑龙江省教育厅面上项目(11521240)
