# Monotonicity condition for the $\theta$-scheme for diffusion equations

## Author Info

• J. Frederic Bonnans

()

(INRIA Saclay - Ile de France - Commands - INRIA - CNRS : UMR7641 - Polytechnique - X - ENSTA ParisTech, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

• Xiaolu Tan

(CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

Registered author(s):

## Abstract

We derive the necessary and sufficient condition for the $L^{\infty}-$monotonicity of finite difference $\theta$-scheme for a diffusion equation. We confirm that the discretization ratio $\Delta t = O(\Delta x^2)$ is necessary for the monotonicity except for the implicit scheme. In case of the heat equation, we get an explicit formula, which is weaker than the classical CFL condition.

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File URL: http://hal.inria.fr/docs/00/63/44/17/PDF/RR-7778.pdf

## Bibliographic Info

Paper provided by HAL in its series Working Papers with number inria-00634417.

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 Length: Date of creation: 21 Oct 2011 Date of revision: Handle: RePEc:hal:wpaper:inria-00634417 Note: View the original document on HAL open archive server: http://hal.inria.fr/inria-00634417/en/ Contact details of provider: Web page: http://hal.archives-ouvertes.fr/

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