Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 42, pp. 1-31.

Title: Sobolev gradients for differential algebraic equations
 
Authors: Robin Nittka   (Univ. of Ulm, Germany)
         Manfred Sauter (Univ. of Ulm, Germany)

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.