☆ 4.6 Article

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

SIAM JOURNAL ON NUMERICAL ANALYSIS (2015)

Journal

SIAM JOURNAL ON NUMERICAL ANALYSIS

Volume 53, Issue 4, Pages 2074-2096

Publisher

SIAM PUBLICATIONS

DOI: 10.1137/140988218

Keywords

end-point singularity; spectral Petrov-Galerkin; collocation; error estimate; Jacobi polynomials; Laguerre polynomials

Categories

Mathematics, Applied

Funding

OSD/MURI grant [FA9550-09-1-0613]
NSF/DMS grant [DMS-1216437]

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Abstract

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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