Time domain solutions to partial differential equations using SPICE

In this paper a method for using a time domain circuit code to solve partial differential equations is described. Rather than following the usual approach of developing a lumped-element circuit model, the partial differential equation is finite differenced in space and written in state variable form. The resulting system of coupled ordinary differential equations is then modeled by an array of coupled voltage dependent current sources connected to a string of capacitors. A preprocessor is used to write the network list in a form usable by the SPICE circuit analysis code. Examples for advection, diffusion, and electromagnetic propagation in one spatial dimension are given.