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

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.