Unconditional Convergence of a Fast Two-Level Linearized Algorithm for Semilinear Subdiffusion Equations
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- 所属单位：理学院
- 发表刊物：J Sci Comput
- 摘要：A fast two-level linearized scheme with nonuniform time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fast L1 formula of the Caputo derivative is derived based on the sum-of-exponentials technique. The resulting fast algorithm is computationally efficient in long-time simulations or small time-steps because it significantly reduces the computational cost O(MN2) and storage O(MN) for the standard L1 formula to O(MNlog N) and O(Mlog N) , respectively, for M grid points in space and N levels in time. The nonuniform time mesh would be graded to handle the typical singularity of the solution near the time t= 0 , and Newton linearization is used to approximate the nonlinearity term. Our analysis relies on three tools: a recently developed discrete fractional Grönwall inequality, a global consistency analysis and a discrete H2 energy method. A sharp error estimate reflecting the regularity of solution is established without any restriction on the relative diameters of the temporal and spatial mesh sizes. Numerical examples are provided to demonstrate the effectiveness of our approach and the sharpness of error analysis. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
- ISSN号：0885-7474
- 是否译文：否
- 发表时间：2019-07-15
- 合写作者：Yan, Yonggui,Zhang, Jiwei
- 通讯作者：廖洪林
- 发表时间：2019-07-15
