Operator splitting for the fractional Korteweg‐de Vries equation.

Our aim is to analyze operator splitting for the fractional Korteweg‐de Vries (KdV) equation, ut=uux+Dαux, α∈[1,2], where Dα=−(−Δ)α/2 is 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 in L2 is obtained for the initial data in H1+α and in case of the Strang splitting, second order convergence in L2 is obtained by estimating the Lie double commutator for initial data in H1+2α. The obtained rates are expected in comparison with the KdV (α=2) case. [ABSTRACT FROM AUTHOR]