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It also includes a description of the respective software; presents illustrative calculations on the example of a reference dynamic system as well as results of computer modeling of real heat exchange processes. The second part of the review is devoted to the Volterra polynomial equations of the first kind. Studies of such equations were pioneered and have been carried out in the past decade by the laboratory of ill-posed problems at ESI SB RAS. A special focus in the paper is made on the importance of the Lambert function for the theory of these equations.<\/p>","DOI":"10.4018\/ijeoe.2013100102","type":"journal-article","created":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T13:02:49Z","timestamp":1392901369000},"page":"16-43","source":"Crossref","is-referenced-by-count":10,"title":["Modeling of Nonlinear Dynamic Systems with Volterra Polynomials"],"prefix":"10.4018","volume":"2","author":[{"given":"A. S.","family":"Apartsyn","sequence":"first","affiliation":[{"name":"Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia"}]},{"given":"S. V.","family":"Solodusha","sequence":"additional","affiliation":[{"name":"Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia"}]},{"given":"V. A.","family":"Spiryaev","sequence":"additional","affiliation":[{"name":"Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia"}]}],"member":"2432","reference":[{"key":"ijeoe.2013100102-0","first-page":"263","author":"A. S.Apartsyn","year":"1987","journal-title":"Discretization methods for regularizing some integral equations of the first kind. Methods of Numerical Analysis and Optimization"},{"key":"ijeoe.2013100102-1","unstructured":"Apartsyn, A. S. (1991). Mathematical modeling of the dynamic systems and objects with the help of the Volterra integral series. 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