| The Ontario Research Centre for Computer Algebra
The UWO ORCCA Reading Room
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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