Abstract
We analyze a fully discrete pseudo-spectral scheme for the numerical solution of the initial-periodic boundary value problem for a nonlinear family of Boussinesq systems. The equations are discretized in space by the Fourier collocation method and in time by an explicit fourth order Runge–Kutta scheme. For the resulting fully discrete scheme, we prove error bounds of spectral accuracy in space and of fourth-order accuracy in time.
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The authors wish to thank David E. Amundsen for many useful discussion on the subject of this paper.
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The authors acknowledge the financial support to this study from the Brazilian research agencies CAPES and CNPq, through the Grants 99999.011638/2013-03 (J.C. Xavier) and 305697/2013-7 (M.A. Rincon), respectively.
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Xavier, J.C., Rincon, M.A. & Alfaro Vigo, D.G. Error estimates for a fully discrete spectral scheme for nonlinear Boussinesq systems. Numer. Math. 149, 679–716 (2021). https://doi.org/10.1007/s00211-021-01239-y
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DOI: https://doi.org/10.1007/s00211-021-01239-y