Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations

We provide an alternative to the Nordsieck technique of changing the stepsize of integration. Order conditions are derived using a recent approach by Albrecht and examples of methods are given which are appropriate for stiff or nonstiff systems in sequential or parallel computing environments. A construction of variable stepsize continuous methods is also described which is facilitated by adding, in general, one extra external stage. Numerical experiments are presented which indicate that the implementation based on variable stepsize formulation is more accurate and more efficient than the implementation based on Nordsieck's technique for second-order DIMSIMs of type 1.