Geodesic
Sobolev gradients for differential algebraic equations
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 65L80, 41A60, 34A09
Keywords: differential algebraic equations, weighted Sobolev gradients, steepest descent, non-linear least squares, consistent initial conditions 
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     author = {Nittka, Robin and Sauter, Manfred},
     title = {Sobolev gradients for differential algebraic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a25/}
}
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Nittka, Robin; Sauter, Manfred. Sobolev gradients for differential algebraic equations. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a25/