How do I solve an ode and plot a graph of two terms within the ode

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Namit Dayal 2023-11-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2048307-how-do-i-solve-an-ode-and-plot-a-graph-of-two-terms-within-the-ode

评论： Torsten 2023-11-23

采纳的回答： Steven Lord

在 MATLAB Online 中打开

I have to plot gamma dot vs tau

where gamma dot can be defined in the range logspace(-3,3,100)

my attempt at this is as follows:

clc, clearvars, close all
eta0 = 8080;
lambda = 1.109;
gamma = logspace(-3, 3, 100);
f = @(t,tau)(-(tau+eta0*gamma)/lambda);
[t, tau] = ode45(@f,[0.001 1000], 0);
loglog(gammaint,tau,'.')

and ive recieved the error messages as follows:

Undefined function 'f' for input arguments of type 'double'.

Error in odearguments (line 92)

f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 104)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode,

tspan, y0, options, varargin);

Error in maxwell5 (line 9)

[t, tau] = ode45(@f,[0.001 1000], 0);

What can i do to fix this,

Thanks

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Sam Chak 2023-11-17

Hi @Namit Dayal

What does the differential equation describe in the real world, and what exactly is the shear rate?

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采纳的回答

Steven Lord 2023-11-16

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2048307-how-do-i-solve-an-ode-and-plot-a-graph-of-two-terms-within-the-ode#answer_1354262

在 MATLAB Online 中打开

eta0 = 8080;
lambda = 1.109;
gamma = logspace(-3, 3, 100);
f = @(t,tau)(-(tau+eta0*gamma)/lambda);

f is already a function handle. So there's no need to specify @f on the next line. Just pass f into ode45. But if you do that you run into a different problem:

[t, tau] = ode45(f,[0.001 1000], 0);
Error using odearguments
@(T,TAU)(-(TAU+ETA0*GAMMA)/LAMBDA) must return a column vector.

Error in ode45 (line 104)
    odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);
loglog(gammaint,tau,'.')

MATLAB calls the ODE function that you pass into ode45 with a vector of values for the second input. If you're trying to solve this for each value of gamma in turn, use a for loop over the elements of gamma. Define f using each element from gamma in turn then call ode45 using that function.

for k = 1:numel(gamma)
    f = @(t,tau)(-(tau+eta0*gamma(k))/lambda);
    [t, tau] = ode45(f, [0.001, 1000], 0);
    % Do something with the t and tau created using this element of gamma
end

If instead you want gamma to be treated as a function of time whose value you only know at specific times, you're going to have to interpolate the value of gamma for the value of t with which ode45 calls the function. See the "ODE with Time-Dependent Terms" example on the ode45 documentation page for an example of this technique.

Finally, I don't know if it's just that you didn't show the definition of the variable or made a typo in the line, but your call to loglog throws an error because gammaint isn't defined.