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Citation bot (talk | contribs) Add: doi, issue, volume. | Use this bot. Report bugs. | Suggested by Abductive | Category:Numerical differential equations | #UCB_Category 116/167 |
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Unlike traditional [[numerical methods for ordinary differential equations|numerical solution methods]], which approach the problem by [[Discretization|discretizing]] time and solving for the next (real-valued) state at each successive time step, QSS methods keep time as a continuous entity and instead [[Quantization (signal processing)|quantize]] the system's state, instead solving for the ''time'' at which the state deviates from its quantized value by a ''quantum''.
They can also have many advantages compared to classical algorithms.<ref>{{cite journal |author1=Migoni, Gustavo |author2=Ernesto Kofman |author3=François Cellier |title=Quantization-based new integration methods for stiff ordinary differential equations|year=2011 |journal = Simulation |volume=88 |issue=4 |pages=387–407 |doi=10.1177/0037549711403645 |url=http://sim.sagepub.com/content/88/4/387 }}</ref>
They inherently allow for modeling discontinuities in the system due to their discrete-event nature and asynchronous nature. They also allow for explicit root-finding and detection of zero-crossing using ''explicit'' algorithms, avoiding the need for iteration---a fact which is especially important in the case of stiff systems, where traditional time-stepping methods require a heavy computational penalty due to the requirement to implicitly solve for the next system state. Finally, QSS methods satisfy remarkable global stability and error bounds, described below, which are not satisfied by classical solution techniques.
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