A comparison of Fourier pseudospectral methods for the solution of the Korteweg-de Vries equation
The paper deals with some numerical approaches to obtain a solution of the Korteweg-de Vries equation \(u_ t+6uu_ x+u_{xxx}=0\) over a time interval from \(t=0\) to \(t=T\) with initial conditions which match the analytic 1-soliton and 2-soliton solutions. The authors use various methods, and for an efficiency comparison the maximum acceptable point- wise error at \(t=T\) is specified and the parameters such as time-step are adjusted to minimize the computing time subject to this error constraint. Pseudospectral methods are also compared from an accuracy viewpoint by investigating how capable they are of reproducing the recurrence phenomenon described by \textit{N. J. Zabusky} and \textit{M. D. Kruskal} [Phys. Rev. Lett. 15, 240 (1965)].
scientific article; zbMATH DE number 4119570
scientific article