PROBLEM 24 - 0591: The population flow between two regions, A and B, is assumed to be proportional to the difference in population density between the areas. Let N¡ (t), N2(t) be the populations in regions A and B respectively, with N1(0) = N10 and N2(0) = N20 . The natural (i.e., in %3D absence of immigration) rates of growth of the regions (per unit of time) are given by the following formulas : Case (1): N = (1) N2 = (b – %3D rN1 %3D mN2/2N20)N2 (2) Case (2): (3) N1 = k(S – N1) N2 = (4) N1 = k(S – 12N2 Case (3): %3D N1) (5) N2 = (b - (6) where r,r2,b,m,k are positive mN2/2N20)N2 constants, 0 < k< 1. Write a FORTRAN program which uses the modified Euler method to simulate this system from t = 0 to t = tf.

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PROBLEM 24 - 0591:
regions, A and B, is
The population flow between two
assumed to be proportional to the
difference in population
density between the areas. Let
N1 (t), N2(t) be the populations
in regions A and B respectively,
with N1 (0) = N1o and
%3D
N2(0) = N20 - The natural (i.e., in
absence of immigration)
rates of growth of the regions (per
unit of time) are given by
the following formulas :
Case (1):
(1)
rN1
N2 = (b -
mN2/2N20)N2
(2)
Case (2):
(3)
Nj = k(S -
N1)
N2 =
(4)
N1 = k(S -
12N2
Case (3):
N7)
(5)
N2 = (b -
(6)
where r,r2,b,m,k are positive
mN2/2N20)N2
constants, 0 < k < 1.
Write a FORTRAN program which
uses the modified Euler
method to simulate this system
from t = 0 to t = tf .
Transcribed Image Text:PROBLEM 24 - 0591: regions, A and B, is The population flow between two assumed to be proportional to the difference in population density between the areas. Let N1 (t), N2(t) be the populations in regions A and B respectively, with N1 (0) = N1o and %3D N2(0) = N20 - The natural (i.e., in absence of immigration) rates of growth of the regions (per unit of time) are given by the following formulas : Case (1): (1) rN1 N2 = (b - mN2/2N20)N2 (2) Case (2): (3) Nj = k(S - N1) N2 = (4) N1 = k(S - 12N2 Case (3): N7) (5) N2 = (b - (6) where r,r2,b,m,k are positive mN2/2N20)N2 constants, 0 < k < 1. Write a FORTRAN program which uses the modified Euler method to simulate this system from t = 0 to t = tf .
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