Displaying similar documents to “Analytical and computational problems in higher special functions”

The Singularity Expansion Method applied to the transient motions of a floating elastic plate

Christophe Hazard, François Loret (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called . This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles of the analytic...

Numerical computation of solitons for optical systems

Laurent Di Menza (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ . In a second part,...

Green’s function pointwise estimates for the modified Lax–Friedrichs scheme

Pauline Godillon (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The aim of this paper is to find estimates of the Green’s function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [27] in the continuous viscous setting.

On numerical solution of multiparameter Sturm-Liouville spectral problems

T. Levitina (1994)

Banach Center Publications

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The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see [2]), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cotθ(x) = y'(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful properties very often being referred to in theoretical research concerning both single- and...