How to solve for the derivative using ode solver

I have the following differential equation

function dRdt = odefun(t,R)

c = 29979245800;

Estart = 10^52;

ni = 10^(-2);

mp = 1.67262192*10^(-24);

T3 = 17*Estart/(8*pi*ni*mp*c^2);

dRdt = sqrt((T3-R^3)*c^2/T3);

end

and I solve it using ode78

[t, R, te, Re, ie] = ode78(@odefun, tspan, r0, options)

thus obtaining R(t). I want to solve the same equation but instead for the derivative (I want to get an array of dRdt and it's corresponding t). How should I go about that?

Thank you in advance!

Answer 1

[Jayant]

Hello @Noya Linder,

To obtain an array of dRdt and its corresponding t values correctly, you can modify the code as follows:

function dRdt = odefun(t, R)
    c = 29979245800;
    Estart = 10^52;
    ni = 10^(-2);
    mp = 1.67262192*10^(-24);
    T3 = 17*Estart/(8*pi*ni*mp*c^2);
    dRdt = sqrt((T3-R^3)*c^2/T3);
end

tspan = [t_start, t_end];
r0 = initial_condition;

options = [];

% Solve the differential equation
[t, R] = ode78(@odefun, tspan, r0, options);

% Calculate dRdt for each time point
dRdt = arrayfun(@odefun, t, R);

This modified code will correctly calculate dRdt for each time point by using the arrayfun function to apply the odefun to each t and R value obtained from the ode78 solver.

You may refer this documentation of arrayfun for reference.

Hope that helps.

[Noya Linder]

Thank you so much! I can't believe the solution was this simple and I made it so complicated in my head lol