how to interpolate the data over uniform time grid

Since numerical solution obtained from ode45 is a non uniform in time, I need to obtain the frequency power spectrim of the solution, but first, i need to interpolate the date over unifrom time grid. How would i able to do so? I am completely stuck after inputting vlause from ODE45! Please explain the steps!

function dxdt = frs(t,x)
dxdt = zeros(3,1);
dx1dt = -((4/5)*x(2)+x(1));     
dx2dt = x(3) + ((4/9)*x(2));  
dx3dt = (1/8)+((x(1)-2.5)*x(2));    
end
tspan = [0:10:100];
xi = [1.0;4.0;2.0];
[t,x]= ode45(@frs,tspan,xi);

from here I do not know how to process with the question please help!

[Walter Roberson]

Since numerical solution obtained from ode45 is a non uniform in time

That is only the case if you pass in a two-element tspan. When you pass in a tspan that is uniform in time, the way you do, then the output from ode45 will only be at those times, and so the output would be uniform in time.

[Mathieu NOE]

you can also interpolate the output data of your ode solution over a new time vector (linear)

use interp1

maybe this will be faster than forcing ode to work on fixed , refined time vector

Answer 1

[Nipun]

Hi [First Name]

I understand that you want to interpolate data over a uniform time grid. Here’s how you can do it using interp1 in MATLAB:

% Given data
time = [0, 1, 4, 5, 6]; % Non-uniform time points
data = [10, 20, 15, 25, 30]; % Corresponding data points

% Uniform time grid
uniformTime = linspace(min(time), max(time), 100);

% Interpolate data over uniform time grid
uniformData = interp1(time, data, uniformTime, 'linear');

% Display results
plot(time, data, 'o', uniformTime, uniformData, '-');
xlabel('Time');
ylabel('Data');
legend('Original Data', 'Interpolated Data');

For more details on interpolation, refer to the MathWorks documentation on interp1: https://www.mathworks.com/help/matlab/ref/interp1.html

Hope this helps.

Regards,

Nipun