Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
| dc.contributor.author | Ferreira González, Chelo | |
| dc.contributor.author | López García, José Luis | |
| dc.contributor.author | Pérez Sinusía, Ester | |
| dc.contributor.department | Ingeniería Matemática e Informática | es_ES |
| dc.contributor.department | Matematika eta Informatika Ingeniaritza | eu |
| dc.date.accessioned | 2020-10-28T10:22:46Z | |
| dc.date.available | 2020-10-28T10:22:46Z | |
| dc.date.issued | 2015 | |
| dc.description.abstract | This paper continues the investigation initiated in [Lopez, 2013]. We consider the asymptotic method designed by F. Olver [Olver, 1974] for linear differential equations of the second order containing a large (asymptotic) parameter . We consider here the second and third cases studied by Olver: differential equations with a turning point (second case) or a singular point (third case). It is well-known that his method gives the Poincar´e-type asymptotic expansion of two independent solutions of the equation in inverse powers of . In this paper we add initial conditions to the differential equation and consider the corresponding initial value problem. By using the Green function of an auxiliary problem, we transform the initial value problem into a Volterra integral equation of the second kind. Then, using a fixed point theorem, we construct a sequence of functions that converges to the unique solution of the problem. This sequence has also the property of being an asymptotic expansion for large (not of Poincar´e-type) of the solution of the problem. Moreover, we show | en |
| dc.description.sponsorship | The Dirección General de Ciencia y Tecnología (REF. MTM2010-21037) is acknowledged for its financial support | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1216/JIE-2015-27-1-27 | |
| dc.identifier.issn | 0897-3962 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/38551 | |
| dc.language.iso | eng | en |
| dc.publisher | Rocky Mountain Mathematics Consortium | en |
| dc.relation.ispartof | Journal of Integral Equations and Applications Volume 27, Number 1 (2015), 27-45. | en |
| dc.relation.publisherversion | https://doi.org/10.1216/JIE-2015-27-1-27 | |
| dc.rights | © 2015 Rocky Mountain Mathematics Consortium | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Second order differential equations. Turning points. Regular singular points. Volterra integral equations of the second kind. Asymptotic expansions. Green functions. Fixed point theorems. Airy functions. Bessel functions. | en |
| dc.title | Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/publishedVersion | |
| dspace.entity.type | Publication | |
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