Optimal convergence of a second order low-regularity integrator for the KdV equation
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In this paper, we establish the optimal convergence result of a second order exponential-type integrator for solving the KdV equation under rough initial data. The scheme is explicit and efficient to implement. By rigorous error analysis, we show that the scheme provides second order accuracy in H^γ for initial data in H^γ+4 for any γ≥0, which is the lowest possible regularity requirement so far. The result is confirmed by numerical experiments and comparisons are made with the Strang splitting scheme.
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