It designs a combined high-order compact method for KdV equation in this work.This method simultaneously and compactly calculates the first-order and third-order spa-tial derivatives which overcomes many shortcomings of classic high-order compact methods.The KdV equation is discretized by the combined high-order compact method in space,and is approximated by the Crank-Nicolson scheme combined with extrapolation method in time.In addition,projection method is used to pull the numerical solution back to the energy-preserving manifold.Finally,some numerical experiments are conducted to verify the numerical accuracy,computational efficiency,and the property of energy-preserving.
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