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Prey-predator system:
the populations of rabbits (x) and foxes (y) follow the following equations:
dx
dt
= !1x − "1xy
dy
dt
= !2y + "2xy
Natural
Death/Birth
Prey/Predator
encounters
00 2 4 6 8 10
10
20
30
40
Time
Population
Rabbit
Foxes
Other numerical methods...
Below are some examples of other numerical methods that we won’t have
time to study in this class.
Partial Differential Equations
➡ A generalization of ODEs to multiple dimensions (time and space)
➡ Example: heat equation in 1D
Eigenvalues and eigenvectors
➡ Compute the eigenvectors and eigenvalues of a matrix.
➡ The solution is based on an iterative process.
➡ If needed in this class, we will just use the Matlab built-in function eig.
!T
!t
= "
!2T
!x2
Conclusions
✓ Numerical methods are an essential part of an engineer’s life.
✓ They allow to solve a much wider range of physical/engineering
problems than analytical methods do.
✓ Numerical methods are however only one part of the solution: a good
physical understanding of the problem is essential.
✓ Numerical methods are the elementary pieces of more complex codes
and software used for scientific simulation.
✓ Studying numerical methods allows one to
- understand how more complex codes work
- be able to modify an existing code or create a new one
- understand the errors/limits introduced by the numerical simulation
FEES of KÖLN BONN AIRPORT
Valid March, 1st 2009
§ 43 LuftVZO
According to the approval ministry of building and traffic NRW dated 18.02.2009.
A. Landing fees
(1) A landing fee is a payable to the airport company by airlines and aircraft
operating agencies for every landing of their aircraft at Cologne/Bonn Airport.
(2) The landing fee is based on
a) the maximum take-off weight* of the aircraft as entered in its certificate of airworthiness,
whereby for landings or take-off between 2200 and 0600 (local time) a
weight of 12,000 kg is taken as the lower limit (fixed fee), regardless of the actual
maximum take-off weight.
A reduction in the MTOW per AFM will only be recognised if advised the FKB** at least
4 months before the beginning of a new schedule period. Appropriate certification
from the German LBA or other competent air-worthiness registration authority is to
be submitted as proof. Every increase in the MTOW of an aircraft in its registration
papers is to be advised the FKB without delay.
For landings during the day and subsequent takeoff between 2200 and 0600 local
time, then the fixed landing fee shall be determined by applying the night time price
(increased MTOW rate).
Cargo-only aircraft are granted a reduction of 25% of the fixed daytime landing fee
from Mondays to Fridays if both take-off and landing are between 0600 and 2200
local time.
and
b) additionally an emission charge per landing
c) additionally a charge for aircraft of noise category ( 1 to 7 )
d) additionally according to the number of passengers on board the aircraft when it
lands an variable fee and passenger fee.
* ) Proof of the applicable MTOW as documented in the aeroplane flight manual (AFM)-Basic Manual-Section for
weight limitations, must be provided.
Failing presentation on the AFM the landing fee will be based on the highest MTOW for the respective type.
Retroactive refunds will not be made.
** ) Flughafen Köln/Bonn GmbH (Cologne/Bonn airport company)
Charges CGN effective 01.03.2009
2
(3)
a) The part of the landing fee based on the maximum take-off weight of the aircraft,
taking into consideration the terms of ICAO (Noise Protection Requirements for Aircraft,
publication of the Federal Aviation Authority of 1 January 1991), is calculated
as follows and amounts to:
aircraft up to 2 t MTOW include emission charge
For propeller aircraft and helicopters
Domestic German and international flights
up to 1.2 t maximum take-off weight over 1.2 to 2 t maximum take-off weight up to 2 t
complying with the complying with the complying with the complying with the without noise
conditions conditions of ICAO, conditions of ICAO, conditions of ICAO, certificate according
of ICAO Appx. 16, Appx. 16, Vol. 1, Chap. 6, Appx. 16, Vol. 1, Appx. 16, Vol. 1, to ICAO Appx. 16,
Vol. 1, Chap. 6 or the LSL, Chap.6 (-4 dB(A)**), Chap.6 *) Vol.1 or the LSL
(-4dB(A)**), Chap. 8, Chap. VI.2.3*) Chap .8, Chap. 10
Chap. 10 or or the LSL
the LSL Chap. VI.2.4., Chap. VIII, Chap. X*)
　
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