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matlabdifferential-equations

Numerical solution of coupled dif eq


So I have a set of 3 differentialequations I want to solve. They can be seen in my code. My problem, is that I want to combine these codes so that I can have a for loop with respect to R (as will be shown.

What I have:

T2 = 1;
[T,Y] = ode45(@ball, [0 5*T2] ,[0 0 -10]);
figure
plot(T,Y(:,1),'-r',T,Y(:,2),'-g',T,Y(:,3),'-b')
legend('x(t)','y(t)','z(t)')
xlabel('Time (in units of T2)')
title(['Plot for RT2 = ',num2str(R)])

Where the @ball is

`function dr = ball(t,b)

T2 = 1;
T1 = T2/2;
d  = 0;
R  = 0.2;

dr = zeros(3,1);
dr(1) = (-1/T2)*b(1)-d*b(2);
dr(2) = (-1/T2)*b(2) + d*b(1) + R*b(3);
dr(3) = (-1/T1)*b(3) - R*b(2) ;

end`

What I want is a single program that will do this, but allow me to include a for loop so I can vary R and make a couple subplots. IS this possible?


Solution

  • You can use an anonymous function for this.

    Change ball.m to remove the hard-coded R and replace it with an input argument:

    function dr = ball(t,b,R)
    
    T2 = 1;
    T1 = T2/2;
    d  = 0;
    %// etc.
    

    and then replace your ode45 call with this:

    R=0.4;
    [T,Y] = ode45(@(t,b) ball(t,b,R), [0 5*T2] ,[0 0 -10]);
    

    where @(t,b) ball(t,b,R) is a function with inputs t and b that calls ball.m with the value of R specified on the previous line. So you can construct the for loop as follows:

    for R=0.2:.02:1 %// or whatever range you want
        [T,Y] = ode45(@(t,b) ball(t,b,R), [0 5*T2] ,[0 0 -10]);
        %// etc.
    end