Rational Krylov subspace methods for phi-functions in exponential integrators

Exponential integrators are a class of numerical methods for stiff systems of differential equations which require the computation of products of so-called matrix phi-functions and vectors. In this thesis, we consider the approximation of these matrix functions times some vector by rational and extended Krylov subspace methods. For arbitrary matrices with a field of values in the left complex half-plane, a uniform approximation is obtained that predicts a sublinear convergence.