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For numerical solution, upwind explicit schemes which have been applied so far generally require extremely small time intervals (10−2 10−3 s) for numerical stability, thus limiting the computational efficiency.
It is well known that for stiff ODE systems explicit schemes can give rise to numerical instability or, alternatively, extremely small time steps.
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First, the number of time-points is extremely small (only 5 time-points), and no replicate data points are available.
The character of the solved set necessitates the use of an extremely small increment of time.
The primary region, the 14.1 MPa to 11,4 MPa interval, presented a steep negative slope and extremely small periods of time indicating high mechanical strength reduction rates at loads near the joints τ u.
There was an extremely small window of time available to create this score so it was a lot of going with your gut.
In the context of sonochemical degradation, cavitation is defined as the cyclic formation, growth, and subsequent collapse of microbubbles or cavities; this cavitation occurs in extremely small intervals of time and releases large quantities of energy over a small location (Gogate 2002).
USM requires extremely small pairwise comparison times, as shown in Table 1, and was thus excluded from this analysis.
It should be noted here that because of their extremely small T2 relaxation times large molecules, such as those present in membranes, proteins, bone and DNA, do not contribute to clinical MR spectra.
Simulational results show that when single tip scratches the surface at an extremely small feed, the second time scratch significantly influences the previous groove.
Thereat, noticing the analogy between the two-level algorithms and the master-slave configuration of PC cluster on one hand, and the suitability of the population-based algorithm like particle swarm optimization (PSO) on the other hand, we have developed a parallel procedure that can make overhead and idle time extremely small, and bring about high performance finally.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com