Time-accurate solutions of Korteweg-de Vries equation using wavelet Galerkin method

In this study we propose a space and time-accurate numerical method for Korteweg-de Vries equation. In deriving the computational scheme, Taylor generalized Euler time discretization is performed prior to wavelet based Galerkin spatial approximation. This leads to the implicit system which can also be solved by explicit algorithms. Korteweg-de Vries equation is also solved by a operator splitting method using wavelet-Taylor-Galerkin approach. Asymptotic stability of the schemes are verified.