论文标题
全局$ h^1 $ h^1 $ - l2-1 $_σ$方法的一般非均匀网格的稳态
Global-in-time $H^1$-stability of L2-1$_σ$ method on general nonuniform meshes for subdiffusion equation
论文作者
论文摘要
在这项工作中，研究子扩散方程的一般不均匀网格的L2-1 $_σ$方法。当时间步长比不少于$ 0.475329 $时，事实证明，与L2-1 $_σ$分数 - 衍生操作员相关的双线性形式被证明是正半数的，并且在简单的假设下是在最初的条件下衍生出的L2-1 $_σ$ Schemes的新全球全球$ H^1 $ - 稳定性。此外，在限制下证明了尖锐的$ l^2 $ norm融合，即时间步长不少于$ 0.475329 $。
In this work the L2-1$_σ$ 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$_σ$ fractional-derivative operator is proved to be positive semidefinite and a new global-in-time $H^1$-stability of L2-1$_σ$ 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 $0.475329$.
