A class of implicit peer methods for stiff systems

We present a class of s-stage implicit two step peer methods for the solution of stiff differential equations using the function values from the previous step in addition to the new function values. This allows to increase the order to p=s and to ensure zero-stability straightforwardly. Corresponding s-stage methods for s≤6 of order p=s with optimal zero stability are presented and their stability is discussed. Under special conditions, we prove that an optimally zero-stable subclass of these methods is superconvergent of order p=s+1 for variable step sizes. Numerical tests and comparison with ode15s show the high potential of this class of implicit peer methods.