Zakharov方程组半离散Fourier谱格式的稳定性

Stability of semi-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,利用Fourier谱方法,在有限时间段[0,T]内,分析Fourier谱格式解的存在性和收敛性,研究半离散Fourier谱格式的稳定性。首先证明了误差eM的L2模,其次证明了eM和ηM的能量模,最后利用Grnwall不等式,借助稳定性的分析方法,证明了Zakharov方程组Fourier谱格式解的稳定性,从而得到了方程组在空间方向上近似解的稳定性结论。

Aimed at studying the solutions of numerical method of Zakharov equations in plasma physics and analyzing the stability of the approximate equations using Fourier spectral method,this paper discusses the stability of semi-discrete Fourier spectral scheme of the equations in [0,T]based on the existence and convergence of the solutions.The paper starts with proving the L2 norm of the error eM,proceeds to prove the energy norm of the error eM and ηM,and ends with proving the stability of Zakharov equations with the stability analysis method using the Grnwall inequality and the conservative nature of the Fourier spectral scheme of the equations,all of which leads to the stability conclusion of the approximate solutions in space.