SDIRK methods for stiff ODEs with oscillating solutions

New SDIRK methods specially adapted to the numerical solution of stiff systems of ODEs which are assumed to possess oscillating solutions are obtained. Our interest is centered on the dispersion (phase errors) and the dissipation (numerical damping), of the dominant components in the numerical oscillations when these methods are applied to a homogeneous linear test model. Two A-stable methods with algebraic order 3 and higher order of dissipation are obtained among the members of a family of methods proposed by Van der Houwen and Sommeijer (1989). Some numerical results are presented to show the efficiency of the new methods when they are compared with other methods presented in Van der Houwen and Sommeijer (1989).