Geodesic
Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1694-1702

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A method for constructing approximate analytic solutions of systems of ordinary differential equations with a polynomial right-hand side is proposed. The implementation of the method is based on the Picard method of successive approximations and a procedure of continuation of local solutions. As an application, the problem of constructing the minimal sets of the Lorenz system is considered. 
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     title = {Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side},
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A. P. Afanas'ev; S. M. Dzyuba. Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1694-1702. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a7/