:Assuming that you have uniform estimates on the truncation error ( e . g ., for a uniformly convergence series ), you can use the method of bisection to locate individual zeros.
32.
Because digital computer mathematics is not perfect, rounding and truncation errors multiply this error, so it is useful to perform an " error analysis " to confirm that values output by the simulation will still be usefully accurate.
33.
And further noting that the quantity on the left is the approximation from the finite difference method and that the quantity on the right is the exact quantity of interest plus a remainder, clearly that remainder is the local truncation error.
34.
If this is not done one is almost certain to see a simulation aborted in the middle of a calculation on a floating point underflow, and if not that bad, still accuracy is likely to get lost due to truncation errors.
35.
This makes the Euler method less accurate ( for small h ) than other higher-order techniques such as Runge-Kutta methods and linear multistep methods, for which the local truncation error is proportional to a higher power of the step size.
36.
For example, in numerical methods for ordinary differential equations, the continuously varying function that is the solution of the differential equation is approximated by a process that progresses step by step, and the error that this entails is a discretization or truncation error.
37.
Even in this case, there is no guarantee that it would converge to the correct solution, because the floating-point round-off or truncation errors can be magnified, instead of damped, causing the deviation from the exact solution to grow exponentially.
38.
For frequencies beyond the end of the pole zero pattern, the group delay suffers a truncation error, but the band edge performance of a characteristic can be improved, by repositioning the outer poles and zeros slightly, to compensate for this sudden termination of the pattern.
39.
The numerical method is " consistent " if the local truncation error is o ( h ) ( this means that for every \ varepsilon > 0 there exists an H such that | \ tau _ n | for all h; see big O notation ).
40.
It confirms that the truncation error of the ( eighth order ) Redfearn series is less than 1 mm out to a longitude difference of 3 degrees, corresponding to a distance of 334 km from the central meridian at the equator but a mere 35 km at the northern limit of an UTM zone.
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