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Math Help - Ordinary Differential Equation Integration in MATLAB

  1. #1
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    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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by nick61416 View Post
    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
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  3. #3
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    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
    Attached Files Attached Files
    Last edited by nick61416; December 8th 2009 at 07:33 PM.
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