Zakharov方程组全离散Fourier谱格式的稳定性  

Stability of full-discrete Fourier spectral scheme for Zakharov equations

作　　者：孙璐[1] 张法勇[2] 陈洪海[1] 王春[1] 

机构地区：[1]黑龙江科技学院理学院,哈尔滨150027 [2]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江科技学院学报》2012年第6期640-644,共5页Journal of Heilongjiang Institute of Science and Technology

基　　金：国家自然科学基金项目(19271025);黑龙江省教育厅科学技术研究项目(12523048)

摘　　要：为研究等离子体物理中Zakharov方程组数值方法解的适定性,讨论了全离散Fourier谱格式的稳定性。首先证明了误差eMn+1的L2模,其次证明了eMn+1和ηMn+1的能量模,最后借助全离散Fourier谱格式的守恒性质,证明了Zakharov方程组全离散Fourier谱格式解的稳定性。该研究改进了半离散Fourier谱格式只在空间方向上的稳定性,得到了全离散Fourier谱格式解在时间方向和空间方向上的稳定性定理。Aimed at studying well-posed problem of the solutions in numerical method of Zakharov equations in plasma physics,this paper discusses the stability of the full-discrete Fourier spectral scheme.The discussion proves the L2 norm of the error eMn＋1,the energy norm of the error eMn＋1 and ηMn＋1,and the stability of the full-discrete Fourier spectral scheme of Zakharov equations with the conservative property.The study contributes to improving the stability of semi-discrete Fourier spectral scheme in space and produces the stability theorem of the approximate solutions in the direction of time and space.

关 键 词：ZAKHAROV方程组 Fourier谱格式 全离散 稳定性 

分 类 号：O241.1[理学—计算数学]