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