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The results are compared with a linearized analysis based on sensitivity analysis about the steady state or metabolic control analysis (MCA).
A linearized analysis is initially used to have an insight into the stability of the balanced steady state of the system.
A linearized analysis shows that the stability of these integration algorithms are determined by the eigenvalues of the local velocity tensor.
The effect of the coupling terms upon the vibration waveforms are investigated by using both a linearized analysis and numerical solution of the differential equations.
Through a linearized analysis in flight dynamics at every instant of time, the Dutch roll motion is found to be in nonlinear oscillation without clear damping of the amplitude.
With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure.
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Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested.
A linearized stability analysis is performed, and the potentiality of the model is illustrated by fabric draping simulations.
A linearized stability analysis, supported by numerical illustrations, reveals that some or all of the limit points may be accessible during fed-batch operation.
The discussion in Higdon (2002) includes the development of the scheme, a linearized stability analysis, a description of some techniques for practical implementation in a nonlinear model, and some numerical testing.
A careful Taylor expansion indicates the second order truncation error of such a splitting approximation, and a linearized stability analysis for the numerical error function yields the desired convergence estimate in the energy norm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com