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 alpha is an element of (0, 1). The scheme is based on a nonuniform L2-1(sigma) formula 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.

Automated summary

An efficient numerical method is proposed for the nonlinear time fractional KdV equation with Caputo fractional derivative, which can effectively handle the weak singularity of the model at t = 0 and has high accuracy. The stability and convergence of the difference scheme are rigorously established, supported by several numerical experiments.