Geodesic
Parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 934-957

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The method of solution continuation with respect to a parameter is used to solve an initial value problem for a system of ordinary differential equations with several limiting singular points. The solution is continued using an argument (called the best) measured along the integral curve of the problem. Additionally, a modified argument is introduced that is locally equivalent to the best one in the considered domain. Theoretical results are obtained concerning the conditioning of the Cauchy problem parametrized by the modified argument in a neighborhood of each point of its integral curve. 
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     author = {E. B. Kuznetsov and S. S. Leonov},
     title = {Parametrization of the {Cauchy} problem for systems of ordinary differential equations with limiting singular points},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a2/}
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E. B. Kuznetsov; S. S. Leonov. Parametrization of the Cauchy problem for systems of ordinary differential equations with limiting singular points. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 934-957. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a2/