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In case of an approximate numerical solution with a rather small error, we propose a geometrical basis and a mathematical algorithm to reconstruct a low-order and low-power polynomial differential equation. To reduce the noise the given time series is smoothed at every point by moving polynomial averages using the least-squares method. Then a specific form of the least-squares method is applied to reconstruct the polynomial right-hand side of the unknown equation. We demonstrate for monotonous, periodic and chaotic solutions that this technique is very efficient.<\/jats:p>","DOI":"10.1142\/s0218127403008715","type":"journal-article","created":{"date-parts":[[2003,12,18]],"date-time":"2003-12-18T09:02:05Z","timestamp":1071738125000},"page":"3307-3323","source":"Crossref","is-referenced-by-count":4,"title":["RECONSTRUCTING DIFFERENTIAL EQUATION FROM A TIME SERIES"],"prefix":"10.1142","volume":"13","author":[{"given":"VALKO","family":"PETROV","sequence":"first","affiliation":[{"name":"Institute of Mechanics, Acad. G. 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