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A stable and accurate explicit scheme for parabolic evolution equations

Summary: A stable and accurate explicit scheme for
parabolic evolution equations
Amir Averbuch Albert Cohen Moshe Israeli
We show that the combination of several numerical techniques,
including multiscale preconditionning and Richardson extrapolation,
yields stable and accurate explicit schemes with large time steps for
parabolic evolution equations. Our theoretical study is limited here to
linear problems (typically the Heat equation with non­constant coeffi­
cients). However, the extrapolation procedures that we study are local
in time, and suggest potential applications to nonlinear problems. In
particular we apply our method to accelerate nonlinear diffusion algo­
rithms for noise removal and segmentation in digital image processing.
1 Introduction
The goal of this paper is to study the combination of several methods in the
numerical treatment of parabolic evolution equations. These methods are:
­Multiscale preconditionning,
­Residual smoothing for iterative schemes,
­Extrapolation methods.
Here, we shall restrict to the simple initial value problem


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences