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Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

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Abstract

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1.0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1.0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

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Notes

  1. For a,b∈ℂ, (6) becomes 2Re(a)+|b|2<0 and (7) becomes Re(2a−b 2)<0.

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Authors and Affiliations

  1. The University of Cambridge, Cambridge, UK

    Jamie Alcock

  2. The University of Queensland, Brisbane, Australia

    Jamie Alcock

  3. COMLAB and Oxford Centre for Integrative Systems Biology, Oxford University and Institute for Molecular Bioscience, Oxford, UK

    Kevin Burrage

  4. Queensland University of Technology, Brisbane, Australia

    Kevin Burrage

Authors
  1. Jamie Alcock
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  2. Kevin Burrage
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Correspondence to Jamie Alcock.

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Communicated by Anders Szepessy.

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Alcock, J., Burrage, K. Stable strong order 1.0 schemes for solving stochastic ordinary differential equations. Bit Numer Math 52, 539–557 (2012). https://doi.org/10.1007/s10543-012-0372-6

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  • DOI: https://doi.org/10.1007/s10543-012-0372-6

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