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

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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https://hal.inria.fr/inria-00634417
Contributor : J. Frederic Bonnans Connect in order to contact the contributor
Submitted on : Friday, October 21, 2011 - 9:49:21 AM
Last modification on : Saturday, June 25, 2022 - 7:39:54 PM
Long-term archiving on: : Thursday, November 15, 2012 - 10:15:33 AM

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  • HAL Id : inria-00634417, version 1

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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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