Improved N-th order averaging theory for periodic systems
The solution x(t;\(\epsilon\)) of a nonlinear periodic system of ordinary differential equations \(\dot x=f(t,x;\epsilon)\), \(x(0;\epsilon)=\xi\), where \(\epsilon\) is a small parameter, is approximated by an N-th order averaging procedure. Under weak smoothness assumptions on the function f(x,t;\(\epsilon\)) the asymptotic solution \(w_ N(t;\epsilon)\) is shown to be \(\epsilon^ N\)-close to the exact solution x(t;\(\epsilon\)) on a time-interval [0,T/\(\epsilon\) ]. The results are very useful for precise investigations of periodic perturbations.
scientific article; zbMATH DE number 4154927