如何在ode45 Matlab中获得dy / dt

Question

I have 2 relations:

y=y0+V*t+sin(w*t)    #relation1
dy/dt=(current/P)-(M1/P)*sin(y)+(M2/P)*sin(y+E)+U*cos(y)*sin(w*t)    #relation2

(M1,P,M2,E,w & U are numerical constants) My goal is to find V(voltage) for different currents. in order to do that, I have to solve relation 2 numerically for different currents, and get dy/dt and then by using the relation between y and V which is <∂y/∂t>=V (<....> denotes a time average), I have to find V. consider that I don`t know the value of dy/dt. I tried this

current = 6e-7 : 1e-8 : 8.5e-7;
for k=1:length(current)
f = @(y, t, M1, P, M2, E) (current(k)/P)-(M1/P)*sin(y)+(M2/P)*sin(y+E)+U*cos(y)*sin(w*t);
[t{k}, y{k}] = ode45(f,tspan,y0);
end

this gives me y for different currents in a cell.

I found out that the following code will give me dy/dt:

ydot=y(:,2)   #if I use 1 instead of 2 it will give me y)

but Now, my problem is changed to this: when I use this code, It will give me dy/dt only for 1 current, how can I get dy/dt for different currents?

Answer 1

Try making your output a vector, where the first element is the state that you are interested in ( y ), and the second element is its derivative with respect to time ( dy/dt ); so y0 = [0;0]; or whatever your starting conditions are. Then make a separate file for your ODE, let's call it "myFcn":

function dydt = myFcn(~, y, M1, P, M2, E, current)      % the ~ is because we are not explicitly dependent on tspan

% Initialize the d/dt vector of our states, y
dydt = zeros(size(y));

% Update the d/dt vector of our states
dydt(1) = y(2);                                         % because (d/dt)y(1) = y(2) = dydt
dydt(2) = current/P - (M1/P)*sin(y) + (M2/P)*sin(y+E);  % your update equation

Now just replace your handle and ode45 call in the above with:

f = @(y, M1, P, M2, E, current(k))myFunc(y, M1, P, M2, E, current(k));
[t{k}, y{k}] = ode45(f, tspan, y0);

Your output will then be the vector y that will give your "position" state y(1) and "velocity" state y(2) . These will be stored in your cell array as before.

Edit:

Updated code to include current(k) , remaining consistent with OP's code.

Answer 2

如果您只是想区分，可以使用f2 = jacobian（f，[dt]）和matlabfunction（f2）来获取函数句柄...