Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time
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.
Keywordsdifferential algebraic equations initial value problems adaptive step-size control Taylor series structural analysis automatic differentiation
AMS subject classification34A09 65L80 68Q25
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