Abstract
Chebyshev methods (also called stabilized methods) are explicit Runge-Kutta methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. We present here new Chebyshev methods of second and fourth order called ROCK, which can be seen as a combination and a generalization of van der Houwen-Sommeijer-type methods and Lebedev-type methods.
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