We construct an iteration sequence converging (in the uniform norm in the space of continuous functions) to the solution of the Cauchy problem for a~singularly perturbed weakly nonlinear differential equation of an arbitrary order (the weak nonlinearity means the presence of a~small parameter in the nonlinear term). The sequence thus constructed is also asymptotic in the sense that the departure of its $n$th element from the solution of the problem is proportional to the $(n+1)$th power of the perturbation parameter.
Singular perturbations, Banach contraction principle, method of asymptotic iterations, Routh-Hurwitz stability criterion
ALIMOV, ALEXEY and BUKHZHALEV, EVGENY
"Iteration method of approximate solution of the Cauchy problem fora~singularly perturbed weakly nonlinear differential equation of an arbitrary order,"
Turkish Journal of Mathematics: Vol. 42:
5, Article 59.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/59