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

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.

KEYWORDS:

• Petrov–Galerkin spectral method
• time fractional KdV equation
• stability
• convergence
• fully discrete scheme

2010 AMS SUBJECT CLASSIFICATION:

• 65M70
• 65M06
• 65M12
• 35R11

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].