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

DOI10.1137/17M1118816zbMATH Open1379.65078arXiv1703.08808MaRDI QIDQ4600008

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Publication date: 5 January 2018

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Abstract: We develop proper correction formulas at the starting $k-1$ steps to restore the desired $k^{mth}$-order convergence rate of the $k$-step BDF convolution quadrature for discretizing evolution equations involving a fractional-order derivative in time. The desired $k^{mth}$-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 $alphain(0,1)$, and sketch the proof for the diffusion-wave case $alphain(1,2)$. Extensive numerical examples are provided to illustrate the effectiveness of the proposed scheme.

Full work available at URL: https://arxiv.org/abs/1703.08808

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