Operator splitting for the fractional Korteweg-de Vries equation

Abstract

Our aim is to analyze operator splitting for the fractional Korteweg-de Vries (KdV) equation, (Formula presented.), (Formula presented.), where (Formula presented.) is a non-local operator with (Formula presented.). 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 (Formula presented.) is obtained for the initial data in (Formula presented.) and in case of the Strang splitting, second order convergence in (Formula presented.) is obtained by estimating the Lie double commutator for initial data in (Formula presented.). The obtained rates are expected in comparison with the KdV (Formula presented.) case. © 2021 Wiley Periodicals LLC.