Integrators for stiff systems with undamped oscillatory solutions

In this paper, we discuss various A-stable integration methods for stiff ordinary differential equations, suitable for general purpose circuit simulations and device simulation. We point out that some of the popular methods either introduce excessive amounts of numerical damping when applied to a loss-less resonance circuit or fail to sufficiently damp rapidly delaying stiff modes. Furthermore, some of these methods can become unstable when applied with variable steps to stable problems with variable coefficients. Some recently discovered integrators, on the other hand, simultaneously combine the advantages and avoid the disadvantages of the former methods. Furthermore, if implemented properly, these latter methods retain their A-stability when applied with variable steps to the stable variable coefficient test equation.