Suppose that the population of Jacobsbaai, a small coastal town on the West Coast of South Africa, was 1000 at the end of the year 2000. Suppose further that the population increased (continuously or steadily) by approximately 5% per year. Then the population can be described by the DE dp dt = 0.05P. Applying two iterations of the 4th Order Runge-Kutta Method with P(0) = 1000, where t = 0 corresponds to the end of the year 2000, and a step size of h = 1 to this problem, yields the following results: Iteration 1:
Suppose that the population of Jacobsbaai, a small coastal town on the West Coast of South Africa, was 1000 at the end of the year 2000. Suppose further that the population increased (continuously or steadily) by approximately 5% per year. Then the population can be described by the DE dp dt = 0.05P. Applying two iterations of the 4th Order Runge-Kutta Method with P(0) = 1000, where t = 0 corresponds to the end of the year 2000, and a step size of h = 1 to this problem, yields the following results: Iteration 1:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:«
Suppose that the population of Jacobsbaai, a small coastal town on the
West Coast of South Africa, was 1000 at the end of the year 2000.
Suppose further that the population increased (continuously or steadily)
by approximately 5% per year. Then the population can be described by
the DE
dP
dt
Applying two iterations of the 4th Order Runge-Kutta Method with
P(0) = 1000, where t = 0 corresponds to the end of the year 2000, and a
step size of h = 1 to this problem, yields the following results:
Iteration 1:
K01
0.05P.
k02
k03
65
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