Numerical Solutions of Index- Differential Algebraic Equations can be Computed in Polynomial Time

The cost of solving an initial value problem for index- differential algebraic equations to accuracy�is polynomial inÐÒ��. 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. AMS subject classification: 34A09, 65L80, 68Q25 Key words: differential algebraic equations, initial value problems, adaptiv