论文标题
对广义Caputo衍生物和广义分数对流扩散方程的高阶近似
High-order approximation to generalized Caputo derivatives and generalized fractional advection-diffusion equations
论文作者
论文摘要
在本文中，认为基于立方插值公式的高阶时间步长方案被认为近似于广义的CAPUTO分数衍生物（GCFD）。该方案的收敛顺序为$（4-α）$，其中$ α〜（0 <α<1）$是GCFD的订单。还提供了本地截断错误。然后，我们采用开发的方案来建立一个差异方案，以解决具有差异边界条件的广义分数对流扩散方程。此外，我们讨论了差异方案的稳定性和收敛性。提出了数值示例以检查理论主张。数值分析差异方案的收敛顺序，时间为$（4-α）$，在空间中为二阶。
In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-α)$, where $α~(0<α<1)$ is the order of the GCFD. The local truncation error is also provided. Then, we adopt the developed scheme to establish a difference scheme for the solution of generalized fractional advection-diffusion equation with Dirichlet boundary conditions. Furthermore, we discuss about the stability and convergence of the difference scheme. Numerical examples are presented to examine the theoretical claims. The convergence order of the difference scheme is analyzed numerically, which is $(4-α)$ in time and second-order in space.
