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

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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Year of publication:	2011-10-21
Authors:	Bonnans, J. Frederic ; Tan, Xiaolu
Institutions:	HAL

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Extent:	application/pdf
Series:	Working Papers.
Type of publication:	Book / Working Paper
Language:	English
Notes:	View the original document on HAL open archive server: http://hal.inria.fr/inria-00634417/en/
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10009325717