To this end, we use
numerical integration of Brzezinski's broad-band Liouville differential equations in celestial frame, in complex form (Brzezinski, 1994):
Another consequence on reducing N is the loss of stability of [[??].sub.N] (t), exemplified in Figure 13 and occurring even after changing the error tolerances of the explicit R-K integrator (the simulations present in this work were performed using the MATLAB[R] integration routine ode45 and, in this specific case, the routines ode113 and ode15s were also tried, all of them resulting in interruption of the
numerical integration).
Mills and Grover's method as well as the
numerical integration one had a practically linear relationship between the increase of a and the increase of the inductance.
As shown in Figure 1, an estimated position and velocity vector of a reentering object is propagated by using a
numerical integration model up to the breakup point at an altitude of 78 km.
If v(x) [member of] [C.sub.2] [a, b], then the error of
numerical integration formula (2) is O([h.sup.2]).
Numerical integration of differential equations of mathematical models of the state of NPP equipment elements taking into account emergent properties.
The obtained formulas for the fields offer advantages in terms of time savings with respect to standard
numerical integration procedures.
A well-known early technique is the selective reduced integration technique [2,3], in which the order of
numerical integration for calculating the shear related part of the stiffness matrix is deliberately reduced.
Among these methods, the Constant method is the simplest but has the lowest accuracy; the Bevis formula is most widely used and especially for real-time applications, but its accuracy may vary with location and season; the approximate integration needs the temperature lapse rate ([alpha]) and vapor pressure decline rate ([lambda]), which cannot be obtained easily, and usually leads to a low accuracy; the
numerical integration is the most accurate method and also easy to be implemented [37].
for the
numerical integration of the MKdV equation (1).