论文标题
关于Korteweg-de Vries方程的高阶完全离散方案的注释，具有runge-kutta-composition类型的时间步骤
Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type
论文作者
论文摘要
我们考虑了Korteweg-de Vries方程的周期性初步问题问题，该方程是我们通过频谱傅立叶 - 盖尔金方法在空间中离散的，并通过隐式，高阶，runge-kutta构图类型的及时基于隐式中点规则进行了及时。我们证明了由此产生的半差异和完全离散的近似值的$ l^{2} $错误估计。
We consider the periodic initial-value problem for the Korteweg-de Vries equation that we discretize in space by a spectral Fourier-Galerkin method and in time by an implicit, high order, Runge-Kutta scheme of composition type based on the implicit midpoint rule. We prove $L^{2}$ error estimates for the resulting semidiscrete and the fully discrete approximations.
