Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side

Method for constructing approximate analytic solutions of differential equations with a polynomial right-hand side

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...

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Veröffentlicht in:Computational mathematics and mathematical physics 2015-10, Vol.55 (10), p.1665-1673
Hauptverfasser: Afanas’ev, A. P., Dzyuba, S. M.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Computational mathematics
Computational Mathematics and Numerical Analysis
Construction
Differential equations
Equality
Exact solutions
Lorenz system
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary differential equations
Polynomials
Studies
Variables
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Beschreibung
Zusammenfassung: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542515100024