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, Volume 41, Issue 2, pp 161171
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Numerical solutions of index1 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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The cost of solving an initial value problem for index1 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 informationbased complexity give exponential cost for solving ordinary differential equations, being based on a different model.
Keywords
differential algebraic equations initial value problems adaptive stepsize control Taylor series structural analysis automatic differentiationAMS subject classification
34A09 65L80 68Q25 Title
 Numerical solutions of index1 differential algebraic equations can be computed in polynomial time
 Journal

Numerical Algorithms
Volume 41, Issue 2 , pp 161171
 Cover Date
 200602
 DOI
 10.1007/s1107500590071
 Print ISSN
 10171398
 Online ISSN
 15729265
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 differential algebraic equations
 initial value problems
 adaptive stepsize control
 Taylor series
 structural analysis
 automatic differentiation
 34A09
 65L80
 68Q25
 Industry Sectors
 Authors

 Silvana Ilie ^{(1)}
 Robert M. Corless ^{(1)}
 Greg Reid ^{(1)}
 Author Affiliations

 1. Ontario Research Centre for Computer Algebra and Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada