Iteration method of approximate solution of the Cauchy problem fora~singularly perturbed weakly nonlinear differential equation of an arbitrary order

Authors

ALEXEY ALIMOV
EVGENY BUKHZHALEV

DOI

10.3906/mat-1807-40

Abstract

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.

Keywords

Singular perturbations, Banach contraction principle, method of asymptotic iterations, Routh-Hurwitz stability criterion

First Page

2841

Last Page

2853

Recommended Citation

ALIMOV, ALEXEY and BUKHZHALEV, EVGENY (2018) "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: No. 5, Article 59. https://doi.org/10.3906/mat-1807-40
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/59