论文标题
对分数进化方程的两个分级时间网格的两种Galerkin离散化的数值分析
Numerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equations
论文作者
论文摘要
分析了分数进化方程的两种具有分级时间网格的数值方法。一个是在分数订单$ 0 <α<1 $的情况下，低阶不连续的Galerkin（DG）离散化，另一个是低阶Petrov Galerkin（PG）离散化，而分数订单$ 1 <α<2 $。通过一种新的二元技术，在合理的规律性假设对初始值的合理定期假设下，DG和PG分别得出了一阶和$（3-α）$ - 级的时间精度的时置误差估计。进行数值实验以验证理论结果。
Two numerical methods with graded temporal grids are analyzed for fractional evolution equations. One is a low-order discontinuous Galerkin (DG) discretization in the case of fractional order $0<α<1$, and the other one is a low-order Petrov Galerkin (PG) discretization in the case of fractional order $1<α<2$. By a new duality technique, pointwise-in-time error estimates of first-order and $ (3-α) $-order temporal accuracies are respectively derived for DG and PG, under reasonable regularity assumptions on the initial value. Numerical experiments are performed to verify the theoretical results.
