A DISCRETE GRONWALL INEQUALITY WITH APPLICATIONS TO NUMERICAL SCHEMES FOR SUBDIFFUSION PROBLEMS
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- 所属单位：理学院
- 发表刊物：SIAM JOURNAL ON NUMERICAL ANALYSIS
- 关键字：fractional subdiffusion equations nonuniform time mesh discrete Caputo derivative discrete Gronwall inequality
- 摘要：We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately resolving the behavior of a solution whose temporal derivatives are singular at t = 0. The main result is a type of fractional Gronwall inequality and we illustrate its use by outlining some stability and convergence estimates of schemes for fractional reaction-subdiffusion problems. This approach extends earlier work that used the familiar L1 approximation to the Caputo fractional derivative, and will facilitate the analysis of higher order and linearized fast schemes.
- ISSN号：0036-1429
- 是否译文：否
- 发表时间：2019-01-01
- 合写作者：McLean, William,Zhang, Jiwei
- 通讯作者：廖洪林
- 发表时间：2019-01-01
