Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time |
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| Authors: | Silvana Ilie Robert M Corless Greg Reid |
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| Institution: | (1) Ontario Research Centre for Computer Algebra and Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada |
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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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| Keywords: | differential algebraic equations initial value problems adaptive step-size control Taylor series structural analysis automatic differentiation |
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