摘要
对Zakharov方程周期边值问题的Fourier谱方法给出了按H^1模的最优误差估计,并获得了关于小参数ε的一致收敛性,数值实验证实了理论分析结果.文中还对一类相关方程的Fourier谱逼近设计了半隐时间离散格式,稳定性好且便于实施.最后,通过与其他数值方法比较,验证了该方法的有效性.
In this paper, the optimal Hi error estimate of the Fourier spectral method for the Zakharov equations with periodic boundary conditions is obtained and, especially, the uniform convergence with respect to the parameter ~ is proved. Also, some semi-implicit time advancing scheme is proposed for the Fourier spectral approximation to a class of relative equations, which is of good stability and can be implemented efficiently. At last, various numerical experiments are conducted to confirm the validity of the method.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2013年第3期409-423,共15页
Acta Mathematica Scientia
基金
国家自然科学基金(11171209)
浙江省教育厅重点项目(z201120169)
上海市教委重点学科建设项目(J50101)资助
