Efficient time-domain solutions using nodal state variables

A method for numerically integrating differential equations, which permits the user to select an integration step without regard to the time constants of the system, is presented. This results in greatly increased numerical efficiency for systems with a wide range of time constants. The method has the further advantage of not being limited to normal form equations or even to first-order equations. The node voltages (and their integrals) thus form a convenient set of state variables. The method consists of formulating and solving the nodal equations at a set of uniformly spaced points in the frequency domain. A simple Laplace transform inversion scheme is used to convert this frequency-domain data to time-domain data. Near-optimal ordering of the nodal equations, together ´with a Gaussian elimination scheme that performs nonzero operations, only results in efficient operation. A simple numerical example is presented to demonstrate the manner in which the parameters of the method control error.