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...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.展开更多
This paper applies exponentially fitted trapezoidal scheme to a stochastic oscillator. The scheme is convergent with mean-square order 1 and symplectic. Its numerical solution oscillates and the second moment increase...This paper applies exponentially fitted trapezoidal scheme to a stochastic oscillator. The scheme is convergent with mean-square order 1 and symplectic. Its numerical solution oscillates and the second moment increases linearly with time. The numerical example verifies the analysis of the scheme.展开更多
基金The Director Innovation Foundation of ICMSEC and AMSS, the Foundation of CAS, the NNSFC (No. 91130003, No. 11021101) and the NSF of Shandong Province (No. ZR2013AQ005, No. BS2013HZ026)
文摘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.
文摘This paper applies exponentially fitted trapezoidal scheme to a stochastic oscillator. The scheme is convergent with mean-square order 1 and symplectic. Its numerical solution oscillates and the second moment increases linearly with time. The numerical example verifies the analysis of the scheme.
