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A new numerical scheme for conservation equations based on evolution byasynchronous discrete events is presented. During each event of the scheme onlytwo cells of the underlying Cartesian grid are active, and an event isprocessed as the exact evolution of this subsystem. This naturally leads to andadaptive scheme in space and time. Numerical results are presented which showthat the error of the asynchronous scheme decreases to zero as a controlparameter is reduced. The construction of the scheme allows it to be expressedas repeated multiplications of matrix exponentials on an initial state vector;thus techniques such as the Goldberg series and the Baker Campbell Hausdorff(BCH) formula can be used to explore the theoretical properties of the scheme.We present the framework of a convergence proof in this manner.

A positivity preserving convergent event based asynchronous PDE solver