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UWO ORCCA TR-05-06 Summary

Polynomial Cost for Solving IVP for High-Index DAE, Robert M. Corless and Silvana Ilie. Submitted October, 2005. (There appears to have been some confusion at the journal end, and an acknowledgement has finally been sent May 31, 2007, after an inquiry).

Abstract: We show that the cost of solving initial value problems for high-index differential algebraic equations is polynomial in the number of digits of accuracy requested. The algorithm analyzed is built on a Taylor series method developed by Pryce for solving a general class of differential algebraic equations. The problem may be fully implicit, of arbitrarily high fixed index and contain derivatives of any order. We also show that adaptive meshes are never more expensive than non-adaptive meshes. Finally, we construct sufficiently smooth interpolants of the discrete solution.

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