A nonlinear and non-local cochlear model has been efficiently solved in the time domain numerically, obtaining the evolution of the transverse displacement of the basilar membrane at each cochlear place. This information allows one to follow the forward and backward propagation of the traveling wave along the basilar membrane, and to evaluate the otoacoustic response from the time evolution of the stapes displacement. The phase/frequency relation of the response can be predicted, as well as the physical delay associated with the response onset time, to evaluate the relation between different cochlear characteristic times as a function of the stimulus level and of the physical parameters of the model. For a nonlinear cochlea, simplistic frequency-domain interpretations of the otoacoustic response phase behavior may give inconsistent results. Time-domain numerical solutions of the underlying nonlinear and non-local full cochlear model using a large number (thousands) of partitions in space and an adaptive mesh in time are rather time and memory consuming. Therefore, in order to be able to use standard personal computers for simulations reliably, the discretized model has been carefully designed to enforce sparsity of the matrices using a multi-iterative approach. Preliminary results concerning the cochlear characteristic delays are also presented.