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Splitting methods with complex coefficients

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Abstract

Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part. In this work we review the composition technique used to construct methods of this class, propose new sixth-order integrators and analyze their main features on a pair of numerical examples, in particular how the errors are propagated along the evolution.

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Authors and Affiliations

  1. Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, E-46022, Valencia, Spain

    Sergio Blanes

  2. Institut de Matemàtiques i Aplicacions de Castelló and Departament de Matemàtiques, Universitat Jaunie I, E-12071, Castellón, Spain

    Fernando Casas

  3. Konputazio Zientziak eta A.A. saila, Informatika Fakultatea, EHU/UPV, Donostia/San Sebastián, Spain

    Ander Murua

Authors
  1. Sergio Blanes
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  2. Fernando Casas
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  3. Ander Murua
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Correspondence to Sergio Blanes.

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Blanes, S., Casas, F. & Murua, A. Splitting methods with complex coefficients. SeMA 50, 47–60 (2010). https://doi.org/10.1007/BF03322541

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