Two FORTRAN packages for assessing initial value methods
ACM Transactions on Mathematical Software (TOMS)
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
The automatic integration of ordinary differential equations
Communications of the ACM
Theory of Modeling and Simulation
Theory of Modeling and Simulation
Quantized-state systems: a DEVS Approach for continuous system simulation
Transactions of the Society for Computer Simulation International - Recent advances in DEVS Methodology--part I
Discrete Event Simulation of Hybrid Systems
SIAM Journal on Scientific Computing
Parallel discrete event simulation with application to continuous systems
Parallel discrete event simulation with application to continuous systems
Continuous System Simulation
A Second Order Accurate Adams-Bashforth Type Discrete Event Integration Scheme
Proceedings of the 21st International Workshop on Principles of Advanced and Distributed Simulation
On the stability and performance of discrete event methods for simulating continuous systems
Journal of Computational Physics
Technical communique: Non-conservative ultimate bound estimation in LTI perturbed systems
Automatica (Journal of IFAC)
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In this paper we introduce new classes of numerical ordinary differential equation (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 primary result of the research described in this article is a first-order accurate QSS-based stiff system solver, called the backward QSS (BQSS). The numerical properties of this new algorithm are 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 the 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, that is, on a stiff system solver based on state quantization.