A four-order alternating segment Crank–Nicolson scheme for the dispersive equation

In this paper, a new alternating segment Crank–Nicolson scheme for the dispersive equation with a periodic boundary condition is derived. The scheme has a four-order truncation error in space and unconditional stability. Its theoretical results are conformed to the numerical simulation. A comparison of the accuracy of this method with the prior ASEI and AGE methods is also included.