Survey of numerical methods for the Korteweg de Vries equation.

Abstract

Numerical methods for solving The Korteweg-de Vries (KdV) equation are studied. Four main classes of numerical methods were implemented and tested; a semi-discretized finite difference method, an iterating finite difference method suggested by Yoshinori Kametaka, the Fourier spectral method and an split-step method. The methods are compared to true solutions for error calculations. The error are discussed both as a function of computational time on a reference computer and as a function of grid points. The methods are also tested on initial conditions who does not have known solutions. The convergence rate and complexity of the implementation are also discussed.