Exponential peer methods

We present a new class of exponential integrators, exponential peer methods, for the solution of stiff differential systems. Order conditions are derived. For a special class of methods of order p = s − 1 , s the number of stages, we show optimal zero stability and prove that for a wide class of stiff systems the methods are of order p ⩾ s − 1 . Numerical tests and comparison with exponential integrators of the Expint package are given. The numerical tests confirm the theoretical results, no order reduction is observed.