摘要
In this paper,we study the convergence rate of an Embedded exponential-type low-regularity integrator(ELRI)for the Korteweg-de Vries equation.We develop some new harmonic analysis techniques to handle the"stability"issue.In particular,we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,|<J^(γ)δx(fg),J^(γ)f>|■||f||H^(γ)^(2)||g||H^(γ+1),and replace f regularity.Based on these techniques,we prove that the ELRI scheme proposed in[41]provides 1/2-order convergence accuracy in H^(γ)for any initial data belonging to H^(γ)with γ>3/2,which does not require any additional derivative assumptions.
