带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式

CRANK-NICOLSON QUASI-COMPACT SCHEMES FOR ONE-SIDED NORMALIZED TEMPERED FRACTIONAL DIFFUSION EQUATIONS WITH DRIFT

基于已有的针对单侧正规化回火分数阶扩散方程的三阶拟紧算法,将该算法的思想应用于带漂移的单侧正规化回火分数阶扩散方程的数值模拟,并结合Crank-Nicolson方法导出数值格式.证明了数值格式的稳定性与收敛性,且数值格式的时间收敛阶和空间收敛阶分别是二阶和三阶.通过数值试验验证了数值格式的有效性和理论结果.

Based on the existed third-order quasi-compact algorithm for one-sided normalized tempered fractional diffusion equations,the idea of the algorithm is applied to the numerical simulation of the one-sided normalized tempered fractional diffusion equations with drift,and combined the Crank-Nicolson method to derive the numerical schemes.The stability and convergence of the numerical schemes are proved,and the time and space convergence orders of the numerical schemes are second and third order,respectively.The effectiveness of the numerical schemes and the theoretical results are verified by numerical experiments.