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López García, José Luis

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https://academica-e.unavarra.es/handle/2454/49435

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López García

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José Luis

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-6050-9015

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2369

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2004 - 20092
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Has files: true × Start date: 2004 × End date: 2009 ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    Formulas for the amplitude of the van der Pol limit cycle through the homotopy analysis method
    (Hindawi / Wiley, 2009) López García, José Luis; Abbasbandy, S.; López Ruiz, R.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Gobierno de Navarra / Nafarroako Gobernua, Res. 07/05/2008
    The limit cycle of the van der Pol oscillator, x¨+ε(x2−1)x˙+x=0, is studied in the plane (x,x˙) by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form of this limit cycle for the whole range of the parameter ε is obtained. These formulas generate the amplitude with an error less than 0.1%. To our knowledge, this is the first time where an analytical approximation of the amplitude of the van der Pol limit cycle, with validity from the weakly up to the strongly nonlinear regime, is given.
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    PublicationOpen Access
    Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials
    (Cambridge University Press, 2004) López García, José Luis; Temme, Nico M.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of functions that are special cases of the given polynomials. The method is based on expanding integrals in one or two points of the complex plane, these points being saddle points of the phase functions of the integrands.