Center of MechanicsStephan Kaufmann



The aim of this package is to show a possible implementation of perturbation methods in Mathematica. It can be used to generate educational examples of perturbation expansions.

The current version of the package covers asymptotic expansions of the solutions of ordinary differential equations (ODE's) with respect to polynomial or general gauge functions (according to the main sources of literature cited above). The methods of straightforward expansions, strained coordinates and matched and composite solutions are implemented.

The method of strained coordinates only uses the simple scheme of Linstedt-Poincaré.

The matching scheme used for matched and composite expansions equals the n-th order asymptotic expansion of the inner solution of order n (transformed to outer coordinates) to the n-th order asymptotic expansion of the outer solution of order n (transformed to inner coordinates).

Up to PerturbationODE


10-Feb-2016 | Stephan Kaufmann | ZfM | ETH