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Title: Correction of high-order BDF convolution quadrature for fractional evolution equations
Authors: Jin, B
Li, B 
Zhou, Z 
Issue Date: 2017
Source: SIAM journal on scientific computing, 2017, v. 39, no. 6, p. A3129-A3152
Abstract: We develop proper correction formulas at the starting k − 1 steps to restore the desired kth-order convergence rate of the k-step BDF convolution quadrature for discretizing evolution equations involving a fractional-order derivative in time. The desired kth-order convergence rate can be achieved even if the source term is not compatible with the initial data, which is allowed to be nonsmooth. We provide complete error estimates for the subdiffusion case α ∈ (0, 1) and sketch the proof for the diffusion-wave case α ∈ (1, 2). Extensive numerical examples are provided to illustrate the effectiveness of the proposed scheme.
Keywords: Backward differentiation formulas
Convolution quadrature
Error estimates
Fractional evolution equation
Incompatible data
Initial correction
Nonsmooth
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on scientific computing 
ISSN: 1064-8275
EISSN: 1095-7197
DOI: 10.1137/17M1118816
Rights: © 2017, Society for Industrial and Applied Mathematics.
Posted with permission of the publisher.
The following publication Jin, B., Li, B., & Zhou, Z. (2017). Correction of high-order BDF convolution quadrature for fractional evolution equations. SIAM Journal on Scientific Computing, 39(6), A3129-A3152 is available at https://dx.doi.org/ 10.1137/17M1118816
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