Numerical Algorithms

, Volume 41, Issue 2, pp 161–171

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


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


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.


differential algebraic equationsinitial value problemsadaptive step-size controlTaylor seriesstructural analysisautomatic differentiation

AMS subject classification


Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Ontario Research Centre for Computer Algebra and Department of Applied MathematicsUniversity of Western OntarioLondonCanada