The primary result of the research described in this article 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 collateral result, a first-order accurate QSS-based solver designed for solving marginally stable systems is briefly outlined as well. This new method, called Centered QSS (CQSS), is successfully applied to a challenging benchmark problem describing a high-order system that is simultaneously 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.
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