Quantization–Based New Integration Methods for Stiff ODEs

The paper introduces new classes of numerical ODE solvers that base their internal discretization method on state quantization instead of time slicing. These solvers have been coined Quantized State System (QSS) simulators. The main result of this work is a first order accurate QSS-based stiff system solver called Backward QSS (BQSS). The numerical properties of this new algorithm are being discussed, and it is shown that this algorithm exhibits properties that make it a potentially attractive alternative to the classical numerical ODE solvers. Some simulation examples illustrate the advantages of this method. As a colateral result, a first order accurate QSS-based solver designed for solving marginally stable systems is sketched. This new method, called Centered QSS (CQSS), is successfully applied to a new difficult benchmark problem describing a high-order system that is simultaneously stiff and marginally stable