ode45 solver loop

Hi. I have to solve this equation

where h is defined by:

My idea is to initialize h=1, solve the first equation, calculate a new value for h:

and do this many times because it guarantees that h has converged. In the Run.m file I do not know how to express the second derivative of R, in fact MATLAB says that Rp is undefined.

Plesset.m file

function Rp = Plesset(t, R)
Rp = zeros(2, 1);
Rp(1) = R(2);
h = 1;
h = 1/R(1)*((R(2)/h)^(1/3) + R(2)/h);
Rp(2) = 1/R(1) * (-1.5 * (R(2))^2 + R(2)/h + sin(t));

Run.m file

for i = 1:100
    [t, R] = ode45('Plesset', [0,5], [0,0]);
    h = R(2)/(R(1)*Rp(2) + 3/2*(R(2))^2 - sin(t));
end
[t, R(:,1)]
plot(t, R(:,1))

Thank you.

Answer 1

[Torsten]

ODE15S can solve differential-algebraic problems. So just use it to solve the two differential equations for R and the algebraic equation for h simultaneously.

To see how this works, look up the section

Solve Robertson Problem as Semi-Explicit Differential Algebraic Equations (DAEs)

under

https://de.mathworks.com/help/matlab/math/solve-differential-algebraic-equations-daes.html

for an example.

Best wishes

Torsten.