Operator splitting for the fractional Korteweg‐de Vries equation

Abstract

AbstractOur aim is to analyze operator splitting for the fractional Korteweg‐de Vries (KdV) equation, , , where is a non‐local operator with . Under the appropriate regularity of the initial data, we demonstrate the convergence of approximate solutions obtained by the Godunov and Strang splitting. Obtaining the Lie commutator bound, we show that for the Godunov splitting, first order convergence in is obtained for the initial data in and in case of the Strang splitting, second order convergence in is obtained by estimating the Lie double commutator for initial data in . The obtained rates are expected in comparison with the KdV case.