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Original Articles

A Petrov–Galerkin spectral method for the linearized time fractional KdV equation

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Pages 1292-1307 | Received 28 Apr 2017, Accepted 18 Oct 2017, Published online: 08 Dec 2017
 

ABSTRACT

In this work, we consider the numerical approximation of a linearized time fractional KdV equation in a bounded domain. A fully discrete scheme combining a Petrov–Galerkin spectral method for the spatial discretization and L1-approximation for the Caputo temporal derivative is proposed. Stability and convergence of the fully discrete scheme are rigourously established. Numerical results are presented to confirm the theoretical results.

2010 AMS SUBJECT CLASSIFICATION:

Acknowledgments

We would like to thank the anonymous referees for their valuable suggestions and comments, which greatly helped improve the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported in part by NSF of China [No. 11401380, No. 11671166, and No. 11701371] and first level discipline project funding in Statistics subject of Shanghai Lixin University of Accounting and Finance [grant no. 2017–10].

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