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Singular Perturbation of Nonlinear Systems with Regular Singularity
Joint Authors
Marchetti, Domingos H. U.
Conti, William R. P.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-29
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Marchetti, Domingos H. U.& Conti, William R. P.. 2018. Singular Perturbation of Nonlinear Systems with Regular Singularity. Discrete Dynamics in Nature and Society،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152666
Modern Language Association (MLA)
Marchetti, Domingos H. U.& Conti, William R. P.. Singular Perturbation of Nonlinear Systems with Regular Singularity. Discrete Dynamics in Nature and Society No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1152666
American Medical Association (AMA)
Marchetti, Domingos H. U.& Conti, William R. P.. Singular Perturbation of Nonlinear Systems with Regular Singularity. Discrete Dynamics in Nature and Society. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1152666
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1152666