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.
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页码：2074 / 2096
页数：23
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