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We investigate dense output formulae (also known as continuous extensions)for strong stability preserving (SSP) Runge-Kutta methods. We require that thedense output formula also possess the SSP property, ideally under the samestep-size restriction as the method itself. A general recipe for first-orderSSP dense output formulae for SSP methods is given, and second-order denseoutput formulae for several optimal SSP methods are developed. It is shown thatSSP dense output formulae of order 3 and higher do not exist, and that in anymethod possessing a second-order SSP dense output, the coefficient matrix A hasa zero row.

Dense output for strong stability preserving Runge-Kutta methods