Electron. J. Diff. Eqns., Vol. 2008(2008), No. 42, pp. 1-31.

Sobolev gradients for differential algebraic equations

Robin Nittka, Manfred Sauter

Abstract:
Sobolev gradients and weighted Sobolev gradients have been used for the solution of a variety of ordinary as well as partial differential equations. In the article at hand we apply this method to linear and non-linear ordinary differential algebraic equations and construct suitable gradients for such problems based on a new generic weighting scheme. We explain how they can be put into practice. In the last part, we discuss the performance of our publicly available implementation on some differential algebraic equations and present further applications.

Submitted March 4, 2008. Published March 20, 2008.
Math Subject Classifications: 65L80, 41A60, 34A09.
Key Words: Differential algebraic equations; weighted Sobolev gradients; steepest descent; non-linear least squares; consistent initial conditions.

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Robin Nittka
University of Ulm
Institute of Applied Analysis, D-89069 Ulm, Germany
email: robin.nittka@uni-ulm.de
Manfred Sauter
University of Ulm
Institute of Applied Analysis, D-89069 Ulm, Germany
email: manfred.sauter@uni-ulm.de

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