Geodesic
Solution of the Cauchy problem. Methods and algorithms
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 70-123

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The problem Cauchy for systems of algebraic-differentional equation with constant coefficients, i.e., for systems of ordinary differential equations that cannot be solved for the highest derivative both regular of index $\gamma>0$ and singular arbitrary $\gamma$ are considered. 
@article{ZNSL_1998_248_a4,
     author = {V. N. Kublanovskaya},
     title = {Solution of the {Cauchy} problem. {Methods} and algorithms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {70--123},
     publisher = {mathdoc},
     volume = {248},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a4/}
}
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V. N. Kublanovskaya. Solution of the Cauchy problem. Methods and algorithms. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIII, Tome 248 (1998), pp. 70-123. http://geodesic.mathdoc.fr/item/ZNSL_1998_248_a4/