An efficient difference scheme for time-fractional KdV equation

In this paper, an efficient numerical method is proposed for the nonlinear time fractional Korteweg–de Vries (KdV) equation with Caputo fractional derivative of order α∈(0,1). The scheme is based on a nonuniform L2-1σformula in time and a second-order finite difference in space. The numerical method can not only effectively deal with the weak singularity of the fractional model at t=0, but also has high accuracy. The stability and convergence of the difference scheme are rigorously established. Finally, several numerical experiments are provided to support the theoretical results.