Singular Perturbation of Nonlinear Systems with Regular Singularity
We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form εzf′=Fε,z,f with F a Cν-valued function, holomorphic in a polydisc D-ρ×D-ρ×D-ρν. We show that its unique formal...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/5163492 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form εzf′=Fε,z,f with F a Cν-valued function, holomorphic in a polydisc D-ρ×D-ρ×D-ρν. We show that its unique formal solution in power series of ε, whose coefficients are holomorphic functions of z, is 1-summable under a Siegel-type condition on the eigenvalues of Ff(0,0,0). The estimates employed resemble the ones used in KAM theorem. A simple lemma is applied to tame convolutions that appear in the power series expansion of nonlinear equations. Applications to spherical Bessel functions and probability theory are indicated. The proposed summability method has certain advantages as it may be applied as well to (singularly perturbed) nonlinear partial differential equations of evolution type. |
|---|---|
| ISSN: | 1026-0226 1607-887X |