多项时间-两边空间分数阶对流-扩散方程的加权隐式数值解

A Weighted Implicit Difference Scheme for Multi-Term Time Fractional Advection-Diffusion Equation with Two-Sided Space Fractional Derivatives

考虑多项时间-两边空间分数阶对流-扩散方程的初边值问题,基于移位Grünwald-Letnikov公式,将方程中的空间分数阶导数采用加权平均有限差分法近似,得到一种加权隐式有限差分格式。利用能量估计,得到了该差分格式的稳定性。然后利用数学归纳法证明了在相同的条件下,所提出的差分格式是收敛的。最后通过数值例子说明了所提出的差分格式是可靠和有效的,并对方程的数值解和精确解进行了比较,验证了本文的理论结果。

A kind of multiple-time two-sided space fractional advection-diffusion equation is considered.Based on the shifted Grünwald-Letnikov formula,the spatial fractional order derivatives in the equations are approximated by the weighted average finite difference method,energy estimation is used,mathematical induction and numerical examples are used to illustrate the reliability and validity of the proposed difference format.A weighted implicit finite difference format,the stability of the difference format,and the convergence of the difference format are achieved.By comparing the numerical and exact solutions of the example equation,the theoretical results are verified.