Solving Diff. Eq. with MATLAB ode45

[klinklindeman]

Hello,

I am trying to write a program on MATLAB using ode45 to solve the following equations:

S'=-bSZ-sS
Z'=bSZ+gR-aSZ
R'=sS+aSZ-gR

These are all derivatives with respect to t, differential equations.

a, b, a and g are all constants.

I realize I need to have two m files, one which defines the functions, and one which calls that and uses ode45. The code for my first m file is:


function Yout = program1(S,Z,R);

global beta gamma alpha sigma;

% set the parmeter values
tend = 10;
S0 = 500;
I0 = 1;
b=0.0095;
g=0.0001;
a= 0.005;
s=0.0001;

Sdot=(-b)*S*Z-(gg*S);

Zdot=(b*S*Z)+(g*R)-(a*S*Z);

Rdot=(s*S)+(a*S*Z)-(g*R);

udot = [Sdot; Zdot; Rdot];

I'm not sure if that is suitable, and I also need help writing the second m file. I need to plot Z and R on the same plot, vs t. I am really stuck, I have been working for hours, looking at examples, trying different combinations. MATLAB is most definitely not my strong point.

Thanks for the help!

 

[NateD]

</code>The first step for solving the equations is to define the functions that describe their derivatives. This can be done in a separate MATLAB script, as you have done above.Next, you need to call the ode45 function. To do this, you will need to create a second MATLAB script. This script should contain the following code:% Define constantsbeta = 0.0095;gamma = 0.0001;alpha = 0.005;sigma = 0.0001;% Set Initial Conditionst0 = 0; S0 = 500; Z0 = 1;R0 = 0;% Solve the differential equations[t,y] = ode45(@program1,[t0,T], [S0,Z0,R0]);% Extract S, Z, and R from yS = y(:,1);Z = y(:,2);R = y(:,3);% Plot the resultsplot(t,Z,t,R);xlabel('Time (t)');ylabel('Population');title('Variation of Z and R with Time');legend('Z','R');In the above code, you call the ode45 function to solve the differential equations with the initial conditions given and the parameters set as global variables. The output of ode45 is then used to plot the resulting populations of Z and R over time.I hope this helps!