Correction of high-order BDF convolution quadrature for fractional evolution equations [article]

Bangti Jin, Buyang Li, Zhi Zhou
2017 arXiv   pre-print
We develop proper correction formulas at the starting k-1 steps to restore the desired k^ th-order convergence rate of the k-step BDF convolution quadrature for discretizing evolution equations involving a fractional-order derivative in time. The desired k^ th-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
more » ... diffusion-wave case α∈(1,2). Extensive numerical examples are provided to illustrate the effectiveness of the proposed scheme.
arXiv:1703.08808v1 fatcat:2j5qvwfg6rawtg6ot7aey6cqaa