  We develop a method for studying the real time dynamics of Heisenberg
operators in strongly-interacting nonequilibrium quantum impurity models. Our
method is applicable to a wide range of interaction strengths and to bias
voltages beyond the linear response regime, works at zero temperature, and
overcomes the finite-size limitations faced by other numerical methods. We
compare our method with quantum Monte Carlo simulations at a strong interaction
strength, at which no analytical method is applicable up to now. We find a very
good coincidence of the results at high bias voltage, and in the short time
period at low bias voltage. We discuss the possible reason of the deviation in
the long time period at low bias voltage. We also find a good coincidence of
our results with the perturbation results at weak interactions.
