The integration of ordinary differential equations: factorization and transformations

Lev M. Berkovich

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 57, issue 3, 175-195

Abstract: This paper is based on a uniform theory of factorization and transformation of nth (n≥2) order ordinary differential equations (ODEs) that are used to constructively solve problems of integrability. This method of factorization of differential operators is developed not only in a base differential field, but also in its algebraic and transcendental extensions. For the first time, the method is extended to nonlinear equations. A new method of exact linearization is proposed that includes transformations used earlier. This method allows us to constructively study nonlinear and nonstationary problems in mathematical simulations with the help of a computer algebra system called REDUCE (as well as other systems).

Keywords: Factorization; Transformation; Differential resultant; Liouvillian solution; Exact linearization (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:57:y:2001:i:3:p:175-195

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