OPTIMAL ERROR ESTIMATES OF SPECTRAL PETROV-GALERKIN AND COLLOCATION METHODS FOR INITIAL VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS

被引：38

作者：

Zhang, Zhongqiang ^{[1
]}

Zeng, Fanhai ^{[2
]}

Karniadakis, George Em ^{[2
]}

机构：

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

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

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2015年 / 53卷 / 04期

关键词：

end-point singularity; spectral Petrov-Galerkin; collocation; error estimate; Jacobi polynomials; Laguerre polynomials; DIFFUSION EQUATION; UNBOUNDED-DOMAINS; ELEMENT METHODS; SPACE; APPROXIMATIONS; POLYNOMIALS; ORDER;

D O I：

10.1137/140988218

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present optimal error estimates for spectral Petrov-Galerkin methods and spectral collocation methods for linear fractional ordinary differential equations with initial value on a finite interval. We also develop Laguerre spectral Petrov-Galerkin methods and collocation methods for fractional equations on the half line. Numerical results confirm the error estimates.

引用

页码：2074 / 2096

页数：23

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