Abstract
We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.
| Original language | English |
|---|---|
| Pages (from-to) | 606-614 |
| Number of pages | 9 |
| Journal | Simulation Series |
| Volume | 54 |
| Issue number | 1 |
| State | Published - 2022 |
| Event | 2022 Annual Modeling and Simulation Conference, ANNSIM 2022 - San Diego, United States Duration: Jul 18 2022 → Jul 20 2022 |
Funding
This manuscript has been authored by UT-Battelle, LLC under Contract No.DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication,acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of the manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). This research was supported in part by an appointment with the National Science Foundation (NSF) Mathematical Sciences Graduate Internship (MSGI) Program sponsored by the NSF Division of Mathematical Sciences. This program is administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and NSF. ORISE is managed for DOE by ORAU. All opinions expressed in this paper are the author's and do not necessarily reflect the policies and views of NSF, ORAU/ORISE, or DOE. This manuscript has been authored by UT-Battelle, LLC under Contract No.DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication,acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of the manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public This research was supported in part by an appointment with the National Science Foundation (NSF) Mathematical Sciences Graduate Internship (MSGI) Program sponsored by the NSF Division of Mathematical Sciences. This program is administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and NSF. ORISE is managed for DOE by ORAU. All opinions expressed in this paper are the author’s and do not necessarily reflect the policies and views of NSF, ORAU/ORISE, or DOE.
| Funders | Funder number |
|---|---|
| DOE Public Access Plan | |
| United States Government | |
| National Science Foundation | |
| U.S. Department of Energy | |
| Division of Mathematical Sciences | |
| Oak Ridge Associated Universities | |
| Oak Ridge Institute for Science and Education |
Keywords
- discrete event simulation
- numerical integration
- quantized state systems