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### SWUFE数学讲坛100：时间分数阶抛物型方程的一些新型数值格式

This talk is concerned with numerical solutions of time-fractional parabolic equations. Due to the Caputo time derivative being involved, the solutions of equations are usually singular near the initial time $t=0$ even for a smooth setting. Based on a simple change of variable $s = t^\beta$, an equivalent $s$-fractional differential equation is derived and analyzed. Then, several novel numerical schemes are presented. Stability and convergence of the schemes are discussed. Finally, numerical comparison are provided with widely used L1-type methods, the CQ methods, and their corrected forms.（本报告主要介绍时间分数阶抛物方程的数值解法。由于Caputo时间分数阶导数使得此类抛物方程的解在初始时刻具有弱奇异性，经过一个变换s = t^\beta, 可以导出$s$-分数阶微分方程, 继而给出一些新的数值格式及其稳定性和收敛性分析。最后，实验将对比所提出的方法与常用的L1-格式，卷积离散方法及校正格式的效果）。