IMPLICIT-EXPLICIT DIFFERENCE SCHEMES FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONSMOOTH SOLUTIONS

被引：69

作者：

Cao, Wanrong ^{[1
]}

Zeng, Fanhai ^{[2
]}

Zhang, Zhongqiang ^{[3
]}

Karniadakis, George Em ^{[2
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[3] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2016年 / 38卷 / 05期

关键词：

time-fractional derivatives; IMEX schemes; low regularity; multirate systems; multiterm fractional derivatives; VOLTERRA INTEGRAL-EQUATIONS; PREDICTOR-CORRECTOR APPROACH; DIFFUSION-EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; SUBDIFFUSION EQUATION; COLLOCATION METHOD; ERROR ANALYSIS; 2ND KIND; TIME; ORDER;

D O I：

10.1137/16M1070323

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order 0 < beta < 1. From the known structure of the nonsmooth solution and by introducing corresponding correction terms, we can obtain uniformly second-order accuracy from these schemes. We prove the convergence and linear stability of the proposed schemes. Numerical examples illustrate the flexibility and efficiency of the IMEX schemes and show that they are effective for nonlinear and multirate fractional differential systems as well as multiterm fractional differential systems with nonsmooth solutions.

引用

页码：A3070 / A3093

页数：24

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