典型文献
Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula
文献摘要：
With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L∞-norm are proved to be 2,3-α,and 4-2α,respectively,where 0＜α＜1.Similarly,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L∞-norm,respectively,where1＜γ＜2.Combining the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results.
文献关键词：
中图分类号：
作者姓名：
Ren-jun Qi;Zhi-zhong Sun
作者机构：
School of Mathematics,Southeast University,Nanjing 210096,Jiangsu,China
文献出处：
引用格式：
[1]Ren-jun Qi;Zhi-zhong Sun-.Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula)[J].应用数学与计算数学学报,2022(04):1313-1350
A类：
Extrapolation,extrapola,where1
B类：
Some,Numerical,Methods,Fractional,Sub,diffusion,Equation,Wave,Based,L1,Formula,With,help,asymptotic,expansion,classic,Li,type,compact,difference,scheme,we,propose,temporal,Richardson,extrapolation,fractional,sub,equation,Three,formulas,are,presented,whose,convergence,orders,norm,proved,be,respectively,Similarly,by,reduction,is,constructed,wave,including,two,which,achieve,Combining,derived,methods,fast,algorithm,Caputo,derivative,sum,exponential,approximation,obtained,reduce,computational,complexity,significantly,while,keep,accuracy,Several,numerical,experiments,confirm,theoretical,results
AB值：
0.568626
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