### Abstract

In this talk, we analyse a family of exponential integrators for second-order differential equations in which high-frequency oscillations in the solution are generated by a linear part. We characterise methods which allow second-order error bounds by presenting a unified error analysis for the whole family of methods. A major advantage of our analysis is that it does not require bounds for point-wise products of matrices and therefore, generalises to abstract differential equations, where the linear part is an unbounded operator with infinitely many large eigenvalues directly.

This is joint work with Volker Grimm