On the Rate of Convergence in Periodic Homogenization of Scalar First-Order Ordinary Differential Equations

On the Rate of Convergence in Periodic Homogenization of Scalar First-Order Ordinary Differential Equations

In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations (ODEs). We provide a quantitative error estimate between the solutions of a first-order ODE with rapidly oscillating coefficients and the solution of the limiting homogenized equation...

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Veröffentlicht in:SIAM journal on mathematical analysis 2010-01, Vol.42 (5), p.2155-2176
Hauptverfasser: Ibrahim, H, Monneau, R
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Convergence
Differential equations
Errors
Estimates
Homogenization
Homogenizing
Mathematical analysis
Mathematics
Ordinary differential equations
Scalars
Studies
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Zusammenfassung:In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations (ODEs). We provide a quantitative error estimate between the solutions of a first-order ODE with rapidly oscillating coefficients and the solution of the limiting homogenized equation. As an application of our result, we obtain an error estimate for the solution of some particular linear transport equations. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/080738830