CORRECTION OF HIGH-ORDER BDF CONVOLUTION QUADRATURE FOR FRACTIONAL EVOLUTION EQUATIONS

被引：170

作者：

Jin, Bangti ^{[1
]}

Li, Buyang ^{[2
]}

Zhou, Zhi ^{[2
]}

机构：

[1] UCL, Dept Comp Sci, Gower St, London WC1E 6BT, England

[2] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2017年 / 39卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

fractional evolution equation; convolution quadrature; initial correction; backward differentiation formulas; nonsmooth and incompatible data; error estimates; DISCONTINUOUS GALERKIN METHODS; DIFFUSION-WAVE EQUATIONS; SPECTRAL METHOD; APPROXIMATIONS; STABILITY; SCHEMES;

D O I：

10.1137/17M1118816

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 alpha is an element of (0, 1) and sketch the proof for the di ff usion-wave case alpha is an element of(1, 2). Extensive numerical examples are provided to illustrate the e ff ectiveness of the proposed scheme.

引用

页码：A3129 / A3152

页数：24

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