Uniform convergence of the legendre spectral method for the Zakharov equations
Uniform convergence of the legendre spectral method for the Zakharov equations
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DOI：
10.1002/num.21716
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发表时间：
2013-03
影响因子：
3.9
通讯作者：
Yuan-yuan Ji;He-ping Ma
中科院分区：
文献类型：
--
作者：
Yuan-yuan Ji;He-ping Ma
给出了标准Zakharov方程在初始边界条件下的Legendre谱近似和拟谱近似。给出了半离散格式和全离散格式的最优H1误差估计。证明了参数ε相对于声速的一致收敛。此外，还构造了可并行实现的多域Legendre谱格式。最后，在单域和多域上的数值结果验证了勒让德谱方法的高精度。©2012 Wiley Percials，Inc.Numer方法偏差分公式2013
The Legendre spectral and pseudospectral approximations are proposed for the standard Zakharov equations with initial boundary conditions. Optimal H1 error estimate of the method is given for both semidiscrete and fully discrete schemes. The uniform convergence for the parameter ε relative to the acoustic speed is proved. Moreover, the multidomain Legendre spectral scheme is also constructed, which can be implemented in parallel. Finally, numerical results in single domain and multidomain verify the high accuracy of the Legendre spectral method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013