Operator splitting for the fractional Korteweg‐de Vries equation

Our aim is to analyze operator splitting for the fractional Korteweg‐de Vries (KdV) equation,u t = uu x + D α u x , α ∈ [ 1 , 2 ] , whereD α = − ( − Δ ) α / 2is a non‐local operator with α ∈ [ 1 , 2 ) . 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 inL 2is obtained for the initial data inH 1 + αand in case of the Strang splitting, second order convergence inL 2is obtained by estimating the Lie double commutator for initial data inH 1 + 2 α. The obtained rates are expected in comparison with the KdV( α = 2 )case.