Giuliani, AndrewKrivodonova, Lilia2018-10-222018-10-222019-01-01https://dx.doi.org/10.1016/j.apnum.2018.08.015http://hdl.handle.net/10012/14042The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.apnum.2018.08.015 © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of lines-type discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. We analyze a fully discrete finite volume method with slope reconstruction and a second order SSP Runge–Kutta time integrator to show that the maximum stable time step can be increased over the SSP limit. Numerical examples indicate that this result extends to two-dimensional problems on triangular meshes.enAttribution-NonCommercial-NoDerivatives 4.0 InternationalCFL conditionHyperbolic conservation lawsMethod of linesStabilityStrong stability preserving methodsArticle