Compact Extrapolation Schemes for a Linear Schrödinger Equation

This paper proposes a kind of compact extrapolation schemes for a linear Schr?dinger equation. The schemes are convergent with fourth-order accuracy both in space and time. Especially, a specific scheme of sixth-order accuracy in space is given. The stability and discrete invariants of the schemes are analyzed. The schemes satisfy discrete conservation laws of original Schr?dinger equation. The numerical example indicates the efficiency of the new schemes.