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We investigate a new class of implicit-explicit singly diagonally implicit Runge-Kutta methods for ordinary dierential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by stage values in the previous step. This approach was rst proposed by the authors in context of implicit-explicit general linear methods

EXTRAPOLATED IMPLICIT–EXPLICIT RUNGE–KUTTA METHODS