# Thread: Ordinary Differential Equation Integration in MATLAB

1. ## Ordinary Differential Equation Integration in MATLAB

Year: 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Pop: 2555 2780 3040 3346 3708 4087 4454 4850 5276 5686 6079

I have this data and i'm asked
(a) Assuming that the above equation holds, use the data from 1950 through 1970 to estimate .
(b) Use the fourth-order Runge-Kutta method, using the value of determined above, to simulate the world population from 1950 to 2050 with a step size of 5 years. Display your simulation results along with the data on the plot.

HINT:
Introduce the incremental year, dx, starting from x=1950 by
dx = x – 1950
so that dx for x=1950 is 0 and dx=20 for x=20 and so on.
Use the world population for dx0=0, 5, 10, 15 and 20 to interpolate p by the Lagrange polynomial.
The derivative of the polynomial is given by another polynomial
>> DC=polyder(C);
which is evaluated at dx0 to give
>> dp0=polyval(DC, dx0);

i am really struggling with this right now any help would be great
thanks

2. Originally Posted by nick61416
Year: 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Pop: 2555 2780 3040 3346 3708 4087 4454 4850 5276 5686 6079

I have this data and i'm asked
(a) Assuming that the above equation holds, use the data from 1950 through 1970 to estimate .
(b) Use the fourth-order Runge-Kutta method, using the value of determined above, to simulate the world population from 1950 to 2050 with a step size of 5 years. Display your simulation results along with the data on the plot.

HINT:
Introduce the incremental year, dx, starting from x=1950 by
dx = x – 1950
so that dx for x=1950 is 0 and dx=20 for x=20 and so on.
Use the world population for dx0=0, 5, 10, 15 and 20 to interpolate p by the Lagrange polynomial.
The derivative of the polynomial is given by another polynomial
>> DC=polyder(C);
which is evaluated at dx0 to give
>> dp0=polyval(DC, dx0);

i am really struggling with this right now any help would be great
thanks
Can we have the full question please?

CB

3. that basically is it here is a little bit more of it
The rate of change of the population p is proportional to the existing population at any time t: dp/dt=Kg*p
where Kg is the growth rate. The world population in millions from 1950 through 2000 was
then the data posted above

edit: i added the whole word document