- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- Iteration method of approximate solution of the Cauchy problem for a~singularly perturbed weakly non...
Iteration method of approximate solution of the Cauchy problem for a~singularly perturbed weakly nonlinear differential equation of an arbitrary order
Authors : Alexey Alimov, Evgeny Bukhzhalev
Pages : 2841-2853
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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