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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.

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

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[2] Mark H. Carpenter , David Gottlieb , and Saul Abarbanel . 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] R. Chen and T. Hagstrom . p-adaptive Hermite methods for initial value problems. ESAIM: Mathematical Modelling and Numerical Analysis, 46:545557, 2012.

[4] X. Chen , D. Appelö , and T. Hagstrom . 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] J. Goodrich , T. Hagstrom , and J. Lorenz . Hermite methods for hyperbolic initial-boundary value problems. Math. Comp., 75:595630, 2006.

[7] M. Hochbruck , C. Lubich , and H. Selhofer . Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput., 19:15521574, 1998.

[8] M. Hochbruck and A. Ostermann . Exponential integrators. Acta Numerica, 19:209286, 2010.

[9] K. Kormann and M. Kronbichler . Parallel finite element operator application: graph partitioning and coloring. 2011 Seventh IEEE International Conference on eScience, pages 332339, 2011.

[10] K. Kormann and E. Larsson . A Galerkin radial basis function method for the Schrödinger equation. SIAM J. Sci. Comput., 35:A2832A2855, 2013.

[11] H.-O. Kreiss and G. Scherer . 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] K. Mattsson and J. Nordström . Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys., 199:503540, 2004.

[13] Anna Nissen , Gunilla Kreiss , and Margot Gerritsen . 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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