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The integration of ordinary differential equations: factorization and transformations

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  • Berkovich, Lev M.

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).

Suggested Citation

  • Berkovich, Lev M., 2001. "The integration of ordinary differential equations: factorization and transformations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(3), pages 175-195.
    • Handle: RePEc:eee:matcom:v:57:y:2001:i:3:p:175-195
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