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Afrika Matematika

, Volume 26, Issue 5–6, pp 761–778 | Cite as

Stability criterion to explicit finite difference applied to the Bresse system

  • Dilberto da S. Almeida JúniorEmail author
  • Jaime E. Muñoz Rivera
Article

Abstract

In this work, we show that the stability criterion of the explicit time integration method applied to the Bresse system is given by
$$\begin{aligned} \Delta t\le \displaystyle \frac{2\epsilon }{\sqrt{ \bigg (12 +\displaystyle \frac{\epsilon ^2}{R^2}\bigg )}\displaystyle \frac{k G}{\rho }}, \end{aligned}$$
where the thickness \(\epsilon \) constitutes a limitation to compute the numerical solutions. This restriction to the stability criterion is not standard (is not CFL condition) and if \(\epsilon <<1\) it is very restrictive to numerical computations. To overcome this restriction, we use the technics performed by Wright [Commun Appl Numer Methods 3:181–185 (1987), Commun Numer Methods Eng 14:81–86 (1998)] to minimize the influence of \(\epsilon \) on stability criterion such that the CFL condition prevails.

Keywords

Finite difference Locking number Energy method Stability criterion 

Mathematics Subject Classification

65L12 65N06 

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Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Dilberto da S. Almeida Júnior
    • 1
    Email author
  • Jaime E. Muñoz Rivera
    • 2
  1. 1.Department of MathematicsFederal University of ParáBelémBrazil
  2. 2.National Laboratory for Scientific ComputationPetrópolisBrazil

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