Methods and apparatus are provided for predicting the number of iterations needed for a computed Transversal Waveform Relaxation solution to achieve a given level of accuracy. In this manner, a Transversal Waveform Relaxation algorithm is disclosed that provides full automation. According to one aspect of the invention, a circuit is analyzed having transmission lines. One or more transmission line parameters of the circuit are obtained, as well as the intrinsic behavior, E(.omega.), and strength of coupling, N(.omega.), of each of the transmission lines. In addition, a relative error bound is obtained for the circuit based on the intrinsic behavior, E(.omega.), and strength of coupling, N(.omega.), of the transmission lines and a predefined error threshold. The process then iterates until the relative error bound satisfies the error threshold.