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A New Class of Highly Accurate Solvers for Ordinary Differential Equations

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Abstract

We introduce a new class of predictor-corrector schemes for the numerical solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs), obtained via the decomposition of the solutions into combinations of appropriately chosen exponentials; historically, such techniques have been known as exponentially fitted methods. The proposed algorithms differ from the classical ones both in the selection of exponentials and in the design of the quadrature formulae used by the predictor-corrector process. The resulting schemes have the advantage of significantly faster convergence, given fixed lengths of predictor and corrector vectors. The performance of the approach is illustrated via a number of numerical examples.

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Authors and Affiliations

  1. Program in Applied Mathematics, Yale University, 51 Prospect St., New Haven, CT, 06511, USA

    Andreas Glaser

  2. Departments of Computer Science and Mathematics, Yale University, 51 Prospect St., New Haven, CT, 06511, USA

    Vladimir Rokhlin

Authors
  1. Andreas Glaser
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  2. Vladimir Rokhlin
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Corresponding author

Correspondence to Andreas Glaser.

Additional information

This work was partially supported by the US Department of Defense under ONR Grant #N00014-07-1-0711 and AFOSR Grants #FA9550-06-1-0197 and #FA9550-06-1-0239.

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Glaser, A., Rokhlin, V. A New Class of Highly Accurate Solvers for Ordinary Differential Equations. J Sci Comput 38, 368–399 (2009). https://doi.org/10.1007/s10915-008-9245-1

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  • DOI: https://doi.org/10.1007/s10915-008-9245-1

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