PARAEXP: a parallel integrator for linear initial-value problems A novel parallel algorithm for the integration of linear initial-value problems is proposed. This algorithm is based on the simple observation that homogeneous problems can typically be integrated much faster than inhomogeneous problems. An overlapping time-domain decomposition is utilized to obtain decoupled inhomogeneous and homogeneous subproblems, and a near-optimal Krylov method is used for the fast exponential integration of the homogeneous subproblems. We present an error analysis and discuss the parallel scaling of our algorithm. The efficiency of this approach is demonstrated with numerical examples.