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Matlab - Numerical Analysis

  1. Oct 7, 2011 #1
    1. The problem statement, all variables and given/known data

    An object of mass m falls from rest at a point near the earth's surface. If the air resistance is proportional to the velocity v^2, the differential equation for the velocity as a function of time is given by m*dv/dt = mg - cv^2

    For the given paraments g = 9.81 m/s^2. m = 68.1 kg and c = 1.5 kg/m. plot the exact solution and the numerical solution v(t) obtained from the 4th order predictor-corrector runge kutta methods using an interval of dt = 0.25 seconds in the domain of 0<t<6

    (I need help with the code of runga kutta, im horrible at matlab


    2. Relevant equations

    m*dv/dt = mg - cv^2


    3. The attempt at a solution



    clear
    clc
    g = 9.81
    m = 68.1
    c = 1.5
    tmax = 6
    dt = 0.25
    t = [0:dt:tmax]
    v(1) =1;

    %Exact Solution
    vs = sqrt(m*g/c)*tanh(t*sqrt(g*c/m));
    plot(t,vs,'s'), hold on

    %Runge-Kutta
    for i = 1:length(t)-1
    f= g - c*v(i).^2/m;
    k1= f(v(i));
    k2= f(t(i)+(dt/2), v(i) + (dt/2)*k1);
    k3 =f(t(i)+(dt/2), v(i) + (dt/2)*k2);
    k4 =f(t(i)+ dt, + v(i) + dt*k3);
    v(i+1) = v(i) + (dt/6)*(k1+2*k2+2*k3+k4);
    end
     
  2. jcsd
  3. Oct 7, 2011 #2
    If you look in the first row of the for loop, the vector v is not defined so the code dosen't make sense.
     
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