A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)

We propose a new class of the exponential propagation iterative methods of RungeKutta-type (EPIRK). The EPIRK schemes are exponential integrators that can be competitive with explicit and implicit methods for integration of large stiff systems of ODEs. Introducing the new, more general then previously proposed, ansatz for EPIRK schemes allows for more flexibility in deriving computationally efficient highorder integrators. Recent extension of the theory of B-series to exponential integrators [1] is used to derive classical order conditions for schemes up to order five. An algorithm to systematically solve these conditions is presented and several new fifth order schemes are constructed. Several numerical examples are used to verify the order of the methods is verified and illustrate the performance of the new schemes.