TY - JOUR
T1 - A Note on the Convergence of a Crank-Nicolson Scheme for the KdV Equation
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 657
EP - 675
PY - 2016
DA - 2016/09
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/458.html
KW - Crank-Nicolson scheme, KdV equation.
AB - <p style="text-align: justify;">The aim of this paper is to establish the convergence of a fully discrete Crank-Nicolson
type Galerkin scheme for the Cauchy problem associated to the KdV equation. The convergence is
achieved for initial data in $L^2$, and we show that the scheme converges strongly in $L^2(0, T; L^2_{loc}(\mathbb{R}))$ to a weak solution for some $T &gt;0$. Finally, the convergence is illustrated by a numerical example.</p>