On the construction of PoincareLindstedt solutions  The nonlinear oscillator equation
Abstract
The equation of motion in a potential energy well Y'' equals F(Y) is formally integrated by a combined power and Fourier series. A new notation is used to reduce the integration problem to the algebraic problem of the solution of two recursion relations in a finite form. Two general algorithms are obtained from the recursion relations for motions in asymmetrical and symmetrical parabolic wells. A third algorithm is presented for the periodic solutions of a form of the EmdenFowler equation. The computer versions of the algorithms for parabolic wells are checked against independent analytical solutions of the equation for timedependent radial motion in the Newtonian twobody problem and the equation of Blasius. The limitations of the solutions to smalltomoderate amplitudes are found by the analyticalcomputer solution of the radial part of the orbital and scattering notions in a LennardJones sixtwelve potential.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 July 1977
 Bibcode:
 1977SJAM...33..161M
 Keywords:

 Differential Equations;
 Nonlinear Equations;
 Operational Calculus;
 Periodic Functions;
 Series Expansion;
 Algorithms;
 Blasius Equation;
 Computer Programs;
 Fourier Series;
 LennardJones Gas;
 Power Series;
 Recursive Functions;
 Physics (General)