- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:24
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
70
2013
1
Convergence of a finite difference method for the KdV and modified KdV equations with $L^2$ data
Paulo
Amorim
Universidade de Lisboa, LISBOA, PORTUGAL
Mário
Figueira
Universidade de Lisboa, LISBOA, PORTUGAL
Korteweg–de Vries equation, KdV equation, finite difference scheme
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 $L^2$), 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.
Numerical analysis
Partial differential equations
General
23
50
10.4171/PM/1924
http://www.ems-ph.org/doi/10.4171/PM/1924