Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time Authors Silvana Ilie Ontario Research Centre for Computer Algebra and Department of Applied Mathematics University of Western Ontario Robert M. Corless Ontario Research Centre for Computer Algebra and Department of Applied Mathematics University of Western Ontario Greg Reid Ontario Research Centre for Computer Algebra and Department of Applied Mathematics University of Western Ontario Article

First Online: 03 December 2005 Accepted: 19 August 2005 DOI :
10.1007/s11075-005-9007-1

Cite this article as: Ilie, S., Corless, R.M. & Reid, G. Numer Algor (2006) 41: 161. doi:10.1007/s11075-005-9007-1
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

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