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

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
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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Reports

Cited literature [2 references]

https://hal.inria.fr/inria-00634417
Contributor : J. Frederic Bonnans <>
Submitted on : Friday, October 21, 2011 - 9:49:21 AM
Last modification on : Wednesday, March 27, 2019 - 4:08:30 PM
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RR-7778.pdf
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• HAL Id : inria-00634417, version 1

### Citation

J. Frederic Bonnans, Xiaolu Tan. Monotonicity condition for the $\theta$-scheme for diffusion equations. [Research Report] RR-7778, INRIA. 2011, pp.6. ⟨inria-00634417⟩

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