Abstract
AbstractRichardson's extrapolation is applied to total variation diminishing (TVD) Runge–Kutta schemes in order to improve their accuracy without doubling their computational cost as classical high‐order (more than three) TVD schemes. The obtained schemes preserve the total variation bounded (TVB) property. Since the extrapolation is performed with schemes that are really TVD, a stable behavior is expected. Using also TVB schemes in space, some numerical experiments showing good performances of the proposed schemes are presented. Up to our knowledge, it is the first time that extrapolation procedures are used in this way. Copyright © 2009 John Wiley & Sons, Ltd.
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