JournalspmVol. 70, No. 1pp. 23–50

Convergence of a finite difference method for the KdV and modified KdV equations with L2L^2 data

  • Paulo Amorim

    Universidade de Lisboa, Portugal
  • Mário Figueira

    Universidade de Lisboa, Portugal
Convergence of a finite difference method for the KdV and modified KdV equations with $L^2$ data cover
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Abstract

We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in L2L^2), without size restrictions. Our approach uses a fourth order (in space) stabilization term and a special conservative discretization of the nonlinear term. Convergence follows from a smoothing effect and energy estimates. We illustrate our results with numerical experiments, including a numerical investigation of an open problem related to uniqueness posed by Y. Tsutsumi.

Cite this article

Paulo Amorim, Mário Figueira, Convergence of a finite difference method for the KdV and modified KdV equations with L2L^2 data. Port. Math. 70 (2013), no. 1, pp. 23–50

DOI 10.4171/PM/1924