56093 20200221144339.0 doi 10.1007/s00365-015-9298-y sideral 92267 ART-2016-92267 eng (orcid)0000-0002-3698-6719 Ferreira, C. Universidad de Zaragoza On a Modification of Olver’s Method: A Special Case 2016 Access copy available to the general public Unrestricted We consider the asymptotic method designed by Olver (Asymptotics and special functions. Academic Press, New York, 1974) for linear differential equations of the second order containing a large (asymptotic) parameter (Formula presented.): (Formula presented.), with (Formula presented.) and g continuous. Olver studies in detail the cases (Formula presented.), especially the cases (Formula presented.), giving the Poincaré-type asymptotic expansions of two independent solutions of the equation. The case (Formula presented.) is different, as the behavior of the solutions for large (Formula presented.) is not of exponential type, but of power type. In this case, Olver’s theory does not give many details. We consider here the special case (Formula presented.). We propose two different techniques to handle the problem: (1) a modification of Olver’s method that replaces the role of the exponential approximations by power approximations, and (2) the transformation of the differential problem into a fixed point problem from which we construct an asymptotic sequence of functions that converges to the unique solution of the problem. Moreover, we show that this second technique may also be applied to nonlinear differential equations with a large parameter. info:eu-repo/grantAgreement/ES/MICINN/MTM2010-21037 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.964 2016 MATHEMATICS 67 / 310 = 0.216 2016 Q1 T1 1.094 2016 Computational Mathematics 2016 Q1 Mathematics (miscellaneous) 2016 Q1 Analysis 2016 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion López, J.L. (orcid)0000-0002-8021-2745 Pérez Sinusía, E. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 43, 2 (2016), 273–290 Constr. approx. CONSTRUCTIVE APPROXIMATION 0176-4276 1108701 http://zaguan.unizar.es/record/56093/files/texto_completo.pdf Postprint 8429 http://zaguan.unizar.es/record/56093/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:56093 articulos driver 2020-02-21-13:48:58 ARTICLE