Accelerating simulation of differential equation systems having continuous behavior

Abstract

An innovative method is taught for accelerating the simulation rate of differential equation systems having behavior piece-wise continuous in both value and time. Specifically, a system of differential equations representing the behavior of a physical system comprised of electronic, optical, or mechanical components may be simulated more rapidly using this method. The method utilizes incremental and iterative reconfiguration of digital logic wherein each configuration of the logic operates to yield a unique future value or range of values for each time-varying state variable within a system of equations representing a linear approximation of the original differential equation system for state variable values defined initially or at the onset of an iteration. Various configurations of the digital logic may be pre-computed or computed on demand, optionally caching such configurations for subsequent reuse.