What is the role of [] in ode?

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채원 이 2022-4-4

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编辑： Stephen23 2022-5-4

Example1)

[t x] = ode45(@fun, tspan, c0,...)

I'm not sure what exactly is [t x] above. As I understand it, does ode represent t,x in [] by unpacking it? Is it exactly solving for x for t?

Example2)

[t x] = ode45(@fun,tspan,c0,...)

[t y] = ode45(@fun,tspan, c0,...)

Does having two odes as above mean solving for x and y? If a function is a function related to x and y (z=x+y), does ode represent the x and y values for t?

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Stephen23 2022-4-6

编辑：Stephen23 2022-5-4

"I'm not sure what exactly is [t x] above."

How to call functions with multiple output arguments:

https://www.mathworks.com/help/matlab/getting-started-with-matlab.html

"As I understand it, does ode represent t,x in [] by unpacking it?"

No, MATLAB does not have any concept of output "unpacking". MATLAB functions can return multple outputs: in the example you show, the function ODE45 two outputs. The names of the variables assigned to those outputs are irrelevant.

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回答（1 个）

Sam Chak 2022-4-4

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在 MATLAB Online 中打开

Hi @채원 이

If the system is

then you can solve the ODEs as follows:

kp = 1;
kd = 2;
F = @(t, x) [x(2); ...
             - kp*x(1) - kd*x(2)];
[t, x] = ode45(F, [0 10], [1, 0]);
plot(t, x)

The solver assigns the solution in the time-vector, t and the

array.

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Stephen23 2022-4-10

编辑：Stephen23 2022-4-10

在 MATLAB Online 中打开

"Is it true that 3 variables (c, t, q in the above function) cannot be solved when solving ode?"

You did not show us an ODE function in any commonly-used mathematical notation. We have no idea what your ODE is.

MATLAB's ODE solvers all solve for vectors of values. You can have as many values in that vector as you wish. If you have three, then it will solve this for you.. If you use indexing inside the objective function to assign them internally to some other variables, then of course you can do that.

As I wrote earlier, you are probably confusing the common use of the word variable with the specific MATLAB meaning. It is easy to use ODE45 to for three input values, you need to think in terms of vectors (not in terms of separately-named variables), for example:

[t,y] = ode45(@myfun, [0,1], [1;2;3])
t = 45×1
         0
    0.0063
    0.0126
    0.0188
    0.0251
    0.0501
    0.0751
    0.1001
    0.1251
    0.1501
y = 45×3
    1.0000    2.0000    3.0000
    1.0507    2.0447    3.0001
    1.1022    2.0910    3.0002
    1.1547    2.1388    3.0005
    1.2082    2.1882    3.0009
    1.4308    2.4017    3.0038
    1.6707    2.6439    3.0085
    1.9299    2.9177    3.0151
    2.2105    3.2263    3.0236
    2.5151    3.5732    3.0340
function dydt = myfun(t,y)
dydt = zeros(2,1);
dydt(1) = y(1)+2*y(2)+y(3);
dydt(2) = 3*y(1)+2*y(2);
dydt(3) = t*y(3);
end