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This is accomplished by approximating the spatial structure of the reactant and autocatalyst concentrations.
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In the last category are indirect methods, such as STICK (Taylor, 2001) and PMML (Konagurthu et al., 2011) which work by approximating the Cα spatial trace using a set of lines.
Approximating the spatial distribution function by a set of Chebyshev orthogonal polynomials, new distributed dynamic loads are constructed with each orthogonal polynomial performing as the spatial distribution function and the previously identified modal load acting as the time history.
For approximating the spatial variable, a new approach which is introduced by Bozzini et al.
Since global bathymetric models are currently available to a very high accuracy and spatial resolution, the errors caused by approximating the actual seawater density by the mean value represent the largest contribution to the total error budget.
The second type of numerical method approximates the equation of interest, usually by approximating the derivatives or integrals in the equation.
In the texture-mapping procedure, we begin by approximating the target surface with an approximating cylinder.
They approximated the spatial derivative by the fourth-order finite difference scheme and the resulted system of second-order ordinary differential equations in time by the implicit Runge-Kutta-Nystrom method, which has fourth-order accuracy in time.
Thus it is likely that the spatial variation of utilization rates for influenza approximates the spatial variation in rates of influenza infection.
This approach, which is the most utilized and has the lowest computational cost, approximates the spatial dependence as an average spatial effect of neighboring areas [ 53].
It is observed that the actual response can be well approximated by the spatial average response only for situations where the critical slip curve is constrained.
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