Article

Numerical Algorithms

, Volume 41, Issue 2, pp 161-171

First online:

Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time

  • Silvana IlieAffiliated withOntario Research Centre for Computer Algebra and Department of Applied Mathematics, University of Western Ontario Email author 
  • , Robert M. CorlessAffiliated withOntario Research Centre for Computer Algebra and Department of Applied Mathematics, University of Western Ontario
  • , Greg ReidAffiliated withOntario Research Centre for Computer Algebra and Department of Applied Mathematics, University of Western Ontario

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Abstract

The cost of solving an initial value problem for index-1 differential algebraic equations to accuracy ɛ is polynomial in ln(1/ɛ). This cost is obtained for an algorithm based on the Taylor series method for solving differential algebraic equations developed by Pryce. This result extends a recent result by Corless for solutions of ordinary differential equations. The results of the standard theory of information-based complexity give exponential cost for solving ordinary differential equations, being based on a different model.

Keywords

differential algebraic equations initial value problems adaptive step-size control Taylor series structural analysis automatic differentiation

AMS subject classification

34A09 65L80 68Q25