Stability analysis for a fully discrete spectral scheme for Boussinesq systems

Abstract

In this paper we perform a stability analysis of a fully discrete numerical method for the solution of a family of Boussinesq systems, consisting of a Fourier collocation spectral method for the spatial discretization and a explicit fourth order Runge–Kutta (RK4) scheme for time integration. Our goal is to determine the influence of the parameters, associated to this family of systems, on the efficiency and accuracy of the numerical method. This analysis allows us to identify which regions in the parameter space are most appropriate for obtaining an efficient and accurate numerical solution. We show several numerical examples in order to validate the accuracy, stability and applicability of our MATLAB implementation of the numerical method.

Keywords:

• Boussinesq system
• Fourier collocation spectral method
• Runge–Kutta scheme
• stability analysis
• numerical experiments

AMS Subject Classifications:

• 65M12
• 65M70
• 35Q35

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

J. C. Xavier was partially supported by CAPES [grant number 99999.011638/2013-03]. M. A. Rincon was partially supported by CNPq [grant number 305697/2013-7].