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Newton polyhedra and power transformations

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  • Bruno, A.D.

Abstract

We give a simple presentation of an algorithm of selecting asymptotical first approximations of equations (algebraic and ordinary differential and partial differential). Here the first approximation of a solution of the initial equation is a solution of the corresponding first approximation of the equation. The algorithm is based on the geometry of power exponents including the Newton polyhedron. The geometry admits transformations induced by power transformations of coordinates. We give also a survey of applications of the algorithms in problems of Celestial Mechanics and Hydrodynamics.

Suggested Citation

  • Bruno, A.D., 1998. "Newton polyhedra and power transformations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(5), pages 429-443.
    • Handle: RePEc:eee:matcom:v:45:y:1998:i:5:p:429-443
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    Cited by:

    1. Khanin, R., 2002. "On the Nipp polyhedron algorithm for solving singular perturbation problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(3), pages 255-272.

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