This thesis presents some new algorithms in the discretetime simulations of non-linear systems with and without dispersive delay-lines. Very computationally efficient algorithms in the simulation of simple and complex dispersive delay-lines are also presented. The technique is then used to simulate injection locking system with strong mutual injection locking factor, which cannot be easily solved be the usual analytical methods. The transient properties of delay-line controlled oscillators have also been investigated, which using existing circuit simulator,e.g. SPICE, is not easily applicable, especially in the cases of non-ideal dispersive delay-lines. During the course of the thesis investigation, a new program for solving circuit solutions in symbolic forms has also been implemented, where it has proven to be very useful in obtaining various analytical solution of circuits and electronic systems. It iaf felt that such a program should complement the usefulnesses of several existing numerical network analysis programs.