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]).
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
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.
The CPU time of MWLS is 53 seconds and the CPU time of EFG is 95 seconds; numerical integration
was no longer necessary for the MWLS method because the CPU time was less than that in the EFG method.
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 .
for the numerical integration
of the MKdV equation (1).