The Computational Complexity of Extrapolation Methods

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Abstract.

This paper analyzes the cost of extrapolation methods for non-stiff ordinary differential equations depending on the number of digits of accuracy requested. Extrapolation of the explicit midpoint rule is applied for various number sequences. We show that for sequences with arithmetic growth, the cost of the method is polynomial in the number of digits of accuracy, while for sequences of numbers with geometric growth, the cost is super-polynomial with respect to the same parameter.

Mathematics Subject Classification (2000).

65L06 68Q25 

Keywords.

Ordinary differential equations initial value problems adaptive step-size control Hölder mean extrapolation 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Numerical Analysis, Centre for Mathematical SciencesLund UniversityLundSweden
  2. 2.Ontario Research Centre for Computer Algebra and Department of Applied MathematicsUniversity of Western OntarioLondonCanada
  3. 3.Department of Applied MathematicsUniversity of Western OntarioLondonCanada

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