A high-order fully discrete scheme for the Korteweg–de Vries equation with a time-stepping procedure of Runge–Kutta-composition type

Abstract

Abstract We consider the periodic initial-value problem for the Korteweg–de Vries equation that we discretize in space by a spectral Fourier–Galerkin method and in time by an implicit, high-order, Runge–Kutta scheme of composition type based on the implicit midpoint rule. We prove $L^{2}$ error estimates for the resulting semidiscrete and the fully discrete approximations. Some numerical experiments illustrate the results.

Locations

• IMA Journal of Numerical Analysis - View
• University of Valladolid Documentary Repository (University of Valladolid) - View - PDF