精品文档---下载后可任意编辑两类空间分数阶偏微分方程模型有限差分逼近的若干讨论中期报告摘要：本文介绍了一类空间分数阶偏微分方程模型，即双分数阶扩散方程模型，和另一类空间分数阶偏微分方程模型，即分数阶扩散–波动联合方程模型。这两个模型都具有分数阶微分算子，需要使用分数阶有限差分方法进行数值逼近。本文着重介绍了基于 Grünwald-Letnikov 型有限差分算子的数值逼近方法，并指出了该方法在模拟分数阶偏微分方程时的稳定性、收敛性以及精确性。另外，本文还介绍了该方法的一些改进，如通过增加交错格点或使用不同的时间步长等方式来改进该方法的精确性。Abstract:This paper introduces two types of spatial fractional partial differential equation models, namely, the double fractional diffusion equation model and the fractional diffusion-wave joint equation model. Both of these models have fractional differential operators and require the use of fractional finite difference methods for numerical approximation. This paper focuses on the numerical approximation method based on the Grünwald-Letnikov type finite difference operator and points out the stability, convergence and accuracy of this method in simulating fractional partial differential equations. In addition, this paper also introduces some improvements to this method, such as improving the accuracy of this method by adding alternating grid points or using different time steps.
