Quantization-Based New Integration Methods for Stiff ODEs

GUSTAVO MIGONI; ERNESTO KOFMAN; FRANÇOIS CELLIER

SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL

SAGE PUBLICATIONS LTD

Año: 2012 vol. 88 p. 387 - 407

0037-5497

The paper introduces new classes of numerical ODE solvers that basetheir internal discretization method on state quantization instead of time slicing. These solvers have been coined Quantized State System (QSS) simulators.The primary result of the research described in this article is afirst-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 collateral result, a first-order accurate QSS-based solver designedfor solving marginally stable systems is briefly outlined as well. Thisnew method, called Centered QSS (CQSS), is successfully applied to achallenging benchmark problem describing a high-order system that issimultaneously stiff and marginally stable.However, the primary emphasis of this article is on the BQSS method,i.e., on a stiff system solver based on state quantization.