Implicit parallel peer methods for stiff initial value problems

A class of implicit two-step integration methods is introduced having s stages which may be computed in parallel. Since all stage solutions are approximations with equal accuracy and stability properties these methods were attributed as 'peer' methods. Using a special result on Vandermonde matrices we identify one subclass of order s−1 which is zero stable for general stepsize sequences. A further analysis for singularly perturbed problems shows that no order reduction occurs and the accuracy is essentially determined by the regularity of the smooth component. These results are backed by several numerical examples even including one differential algebraic problem.