Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
任金城 教授, 河南财经政法大学 数学与信息学院
Inviter:
郑伟英
Title:
Sharp $H^1$-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
Time & Venue:
2018.8.31 10:00-11:00 Z311
Abstract:
Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional $H^1$-norm analysis (corresponding to the case for a classical diffusion equation) to the time approximations of a fractional subdiffusion problem always leads to suboptimal error estimates (a loss of time accuracy). To recover the theoretical accuracy in time, we propose an improved discrete Gr\"{o}nwall inequality and apply it to the well-known L1 formula and a fractional Crank-Nicolson scheme. With the help of a time-space error-splitting technique and the global consistency analysis, sharp $H^1$-norm error estimates of the two nonuniform approaches are established for a reaction-subdiffusion problems. Numerical experiments are included to confirm the sharpness of our analysis.This is the joint work with Hong-lin Liao, Jiwei Zhang and Zhimin Zhang.