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

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.

DOI

10.3906/mat-1807-40

Keywords

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

First Page

2841

Last Page

2853

Recommended Citation

ALIMOV, A, & BUKHZHALEV, E (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 42 (5): 2841-2853. https://doi.org/10.3906/mat-1807-40