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An Explicit Hermite-Taylor Method for the Schrödinger Equation

  • Daniel Appelö (a1), Gunilla Kreiss (a2) and Siyang Wang (a2)

An explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method.

Corresponding author
*Corresponding author. Email addresses: (D. Appelö), (G. Kreiss), (S.Wang)
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Communicated by Chi-Wang Shu

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[1] AppelöD. and HagstromT.. On advection by Hermite methods. Paciffic Journal Of Applied Mathematics, 4(2):125139, 2011.
[2] CarpenterMark H., GottliebDavid, and AbarbanelSaul. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. J. Comput. Phys., 111(2):220236, 1994.
[3] ChenR. and HagstromT.. p-adaptive Hermite methods for initial value problems. ESAIM: Mathematical Modelling and Numerical Analysis, 46:545557, 2012.
[4] ChenX., AppelöD., and HagstromT.. A hybrid Hermite–discontinuous Galerkin method for hyperbolic systems with application to Maxwell's equations. Journal of Computational Physics, 257, Part A:501520, 2014.
[5] GoodrichJ., HagstromT., and LorenzJ.. Hermite methods for hyperbolic initial-boundary value problems. Math. Comp., 75:595630, 2006.
[6] HagstromT. and AppelöD.. Solving PDEs with Hermite Interpolation. In Springer Lecture Notes in Computational Science and Engineering, 2015.
[7] HochbruckM., LubichC., and SelhoferH.. Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput., 19:15521574, 1998.
[8] HochbruckM. and OstermannA.. Exponential integrators. Acta Numerica, 19:209286, 2010.
[9] KormannK. and KronbichlerM.. Parallel finite element operator application: graph partitioning and coloring. 2011 Seventh IEEE International Conference on eScience, pages 332339, 2011.
[10] KormannK. and LarssonE.. A Galerkin radial basis function method for the Schrödinger equation. SIAM J. Sci. Comput., 35:A2832A2855, 2013.
[11] KreissH.-O. and SchererG.. Finite element and finite difference methods for hyperbolic partial differential equations. In Mathematical Aspects of Finite Element in Partial Differential Equations. Academic Press, Inc., 1974.
[12] MattssonK. and NordströmJ.. Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys., 199:503540, 2004.
[13] NissenAnna, KreissGunilla, and GerritsenMargot. High order stable finite difference methods for the Schrödinger equation. J. Sci. Comput., 55:173199, 2013.
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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