Projective Integration with an Adaptive Projection Horizon

Abstract

We present an algorithm for projective integration that is computationally efficient for integrating systems of differential equations with multiple time-scales. Adaptive projective integration is a technique that uses a few inner integration steps to generate data to fit to a local reduced-order model. This reduced-order model is then used to extrapolate forward in time to estimate the states at some future time. This inner-outer integration is iterated until the desired integration is complete. The method uses an adaptive projective horizon to control for error generation during the integration. By examining an example Brusselator system, consisting of three non-linear differential equations, we show two orders of magnitude savings in computational time using adaptive projective integration over explicit Euler's method.