Geodesic
Application of the least square method to the solving linear differential-algebraic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 81-95.

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We consider application of the least square method to the numerical solution of a linear system of ordinary differential equations (ODEs) with an identically singular matrix multiplied a higher derivative by the desired vector-function. We discuss the behavior of the gradient method for minimizing the functional of the residual square in the Sobolev space and some other issues. The results of the numerical experiments are given. 
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V. F. Chistyakov; E. V. Chistyakova. Application of the least square method to the solving linear differential-algebraic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a8/

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