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
收藏
页码：2074 / 2096
页数：23
相关论文
共 45 条
[1]  
Adams R., 1975, SOBOLEV SPACES
[2]  
Alpert Bradley K., 1991, SIAM J SCI STAT COMP, V12, P12
[3]  
[Anonymous], 1991, J. Integral Equations Appl.
[4]  
[Anonymous], 1997, Fractals and Fractional Calculus in Continuum Mechanics
[5]   INTEGRAL REPRESENTATIONS FOR JACOBI POLYNOMIALS AND SOME APPLICATIONS [J].
ASKEY, R ;
FITCH, J .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1969, 26 (02) :411-&
[6]   DUAL EQUATIONS AND CLASSICAL ORTHOGONAL POLYNOMIALS [J].
ASKEY, R .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1968, 24 (03) :677-&
[7]  
Askey R., 1975, Orthogonal polynomials and special functions, V1st ed.
[8]  
Baleanu D., 2013, ABSTR APPL ANAL, V413529, P12
[9]  
Boyd J., 2001, Chebyshev and fourier spectral methods, V2nd
[10]   hp-discontinuous Galerkin time-stepping for Volterra integrodifferential equations [J].
Brunner, H ;
Schötzau, D .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (01) :224-245
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