期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 56, 期 2, 页码 1112-1133出版社
SIAM PUBLICATIONS
DOI: 10.1137/17M1131829
关键词
fractional subdiffusion equations; nonuniform L1 formula; discrete fractional Gronwall inequality; global consistency analysis; sharp error estimate
资金
- NUAA Scientific Research Starting Fund of Introduced Talent [1008-YAH18037]
- 333 High-level Personal Training Project of Jiangsu Province [DRA2015518]
- NSFC [11372354, 11771162, CityU11302915, 11771035, 91430216]
- NSAF [U1530401]
Stability and convergence of the L1 formula on nonuniform time grids are studied for solving linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional Gronwall inequality is developed for the nonuniform L1 formula by introducing a discrete convolution kernel of Riemann-Liouville fractional integral. To simplify the consistency analysis of the nonuniform L1 formula, we bound the local truncation error in a discrete convolution form and consider a global convolution error involving the discrete Riemann-Liouville integral kernel. With the help of discrete fractional Gronwall inequality and global consistency error analysis, a sharp error estimate reflecting the regularity of solution is obtained for a simple L1 scheme. Numerical examples are provided to verify the sharpness of the error analysis.
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