Some algebras associated with asymptotic methods of nonlinear mechanics
Abstract
Asymptotic solution algorithms are developed for a certain class of equations describing nonlinear oscillations, including the Van der Pol equation. It is shown that asymptotic solutions for this class of equations can be obtained by computation in certain algebras which are distributive halfrings. Attention is given to operations of differentiation, integration, and Fourier series expansion in such algebras.
 Publication:

Ukrainskii Matematicheskii Zhurnal
 Pub Date:
 1980
 Bibcode:
 1980UkMaZ..32..252S
 Keywords:

 Algebra;
 Asymptotic Methods;
 Group Theory;
 Mechanical Oscillators;
 Nonlinear Equations;
 Rings (Mathematics);
 Algorithms;
 Differential Equations;
 Fourier Series;
 Roots Of Equations;
 Series Expansion;
 Physics (General)