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

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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.

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Authors and Affiliations

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

    Silvana Ilie, Robert M. Corless & Greg Reid

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  1. Silvana Ilie
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  2. Robert M. Corless
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  3. Greg Reid
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Correspondence to Silvana Ilie.

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Ilie, S., Corless, R.M. & Reid, G. Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time. Numer Algor 41, 161–171 (2006). https://doi.org/10.1007/s11075-005-9007-1

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  • DOI: https://doi.org/10.1007/s11075-005-9007-1

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