Prof. Dongfang LI
School of Mathematics and Statistics
Huazhong University of Science and Technology
An essential feature of the subdiffusion equations with the α-order time fractional derivative is the weak singularity at the initial time. The weak regularity of the solution is usually characterized by a regularity parameter δ∈(0,1)∪(1,2). Under this general regularity assumption, we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results, i.e., a refined discrete fractional-type Gronwall inequality. After that, we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations. The present results fill the gap on some interesting convergence results of L1 scheme on δ∈(0,α)∪(α,1)∪(1,2]. Numerical experiments are provided to demonstrate the effectiveness of our theoretical analysis.
Prof. Dongfang LI obtained his Ph.D. degree in Huazhong University of Science and Technology in 2011 and did post-doctoral research at McGill University and City University of Hong Kong. His main research interests include numerical analysis , fractional differential equations, etc.
He is a professor at the School of Mathematics and Statistics, Huazhong University of Science and Technology, has published more than 30 papers on many international famous SCI journals of computing, such as J. Comp. Phys., Appl. Comp. Harm. Appl., J. Sci. Comp.