In this work the L2-1$_\sigma$ method on general nonuniform meshes is studied for the subdiffusion equation. When the time step ratio is no less than $0.475329$, a bilinear form associated with the L2-1$_\sigma$ fractional-derivative operator is proved to be positive semidefinite and a new global-in-time $H^1$-stability of L2-1$_\sigma$ schemes is then derived under simple assumptions on the initial condition and the source term. In addition, the sharp $L^2$-norm convergence is proved under the constraint that the time step ratio is no less than $0.475329$.
翻译:在这项工作中,为子扩散方程式研究关于一般非统一模格的L2-1$QQgma$方法,当时间档比率不少于0.475329美元时,与L2-1$Qgma$分位衍生操作器有关的双线表被证明是正半无限期的,然后根据对初始条件和来源术语的简单假设,得出一个新的全球时值为H1$L2-1$gma$的稳定性方案,此外,在时间档比率不低于0.475329美元的制约下,证明了急剧的L2$-诺姆趋同。