Lindstedt’s Method

Abstract

Lindstedt’s perturbation method is a classical scheme for obtaining approximate solutions to differential equations which contain a small parameter e. The idea is to expand the solution in a power series in ∈,

$$ x\left( t \right) = {x_0}\left( t \right) + {x_1}\left( t \right) \in + {x_2}\left( t \right){ \in ^2} + \cdot\cdot\cdot $$

(1)

and to solve for the unknown functions x_i(t) recursively, i.e., in the order x₀(t), x_l(t), x₂(t), . . ..