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Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations

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. 10.1137/17M1118816. Green open access

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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.

Type: Article
Title: Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/17M1118816
Publisher version: https://doi.org/10.1137/17M1118816
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: fractional evolution equation, convolution quadrature, initial correction, backward differentiation formulas, nonsmooth and incompatible data, error estimates
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/10023361
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