  To integrate large systems of nonlinear differential equations in time, we
consider a variant of nonlinear waveform relaxation (also known as dynamic
iteration or Picard-Lindel\"of iteration), where at each iteration a linear
inhomogeneous system of differential equations has to be solved. This is done
by the exponential block Krylov subspace (EBK) method. Thus, we have an
inner-outer iterative method, where iterative approximations are determined
over a certain time interval, with no time stepping involved. This approach has
recently been shown to be efficient as a time-parallel integrator within the
PARAEXP framework. In this paper, convergence behavior of this method is
assessed theoretically and practically. We examine efficiency of the method by
testing it on nonlinear Burgers, three-dimensional Liouville-Bratu-Gelfand, and
three-dimensional nonlinear heat conduction equations and comparing its
performance with that of conventional time-stepping integrators.
