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.

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Yin, X. (2014) Compact Extrapolation Schemes for a Linear Schrödinger Equation. American Journal of Computational Mathematics, 4, 206-212. doi: 10.4236/ajcm.2014.43017.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Wusu, A.S., Akanbi, M.A. and Okunuga, S.A. (2013) A Three-Stage Multiderivative Explicit Runge-Kutta Method. American Journal of Computational Mathematics, 3, 121-126.
[2] Shiferaw, A. and Mittal, R.C. (2014) High Accurate Fourth-Order Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate. American Journal of Computational Mathematics, 4, 73-86.
[3] Hong, J. and Li, C. (2006) Multi-Symplectic Runge-Kutta Methods for Nonlinear Dirac Equations. Journal of Computational Physics, 211, 448-472.
[4] Lele, S.K. (1992) Compact Finite Difference Schemes with Spectral-Like Solution. Journal of Computational Physics, 103, 16-42.
[5] Ma, Y., Kong, L. and Hong, J. (2011) High-Order Compact Splitting Multisymplectic Method for the Coupled Nonlinear Schrodinger Equations. Computers & Mathematics with Applications, 61, 319-333.
[6] Sekhar, T., Raju B. (2012) An Efficient Higher Order Compact Scheme to Capture Heat Transfer Solutions in Spherical Geometry. Computer Physics Communications, 183, 2337-2345.
[7] Phillips, A. (2003) Introduction to Quantum Mechanics. Wiley, Chichester.
[8] Hong, J. and Kong, L. (2010) Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrodinger Equation with Trapped Term. Communications in Computational Physics, 7, 613-630.
[9] Hong, J., Liu, X. and Li, C. (2007) Multi-Symplectic Runge-Kutta-Nystrom Methods for Nonlinear Schrodinger Equations with Variable Coefficients. Journal of Computational Physics, 226, 1968-1984.
[10] Kong, L., Hong, J., Wang, L. and Fang, F. (2009) Symplectic Integrator for Nonlinear High Order Schrodinger Equation with a Trapped Term. Journal of Computational and Applied Mathematics, 231, 664-679.

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