ode45 solver loop

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Marco Sammito
Marco Sammito 2016-11-9
回答： Torsten 2016-11-9
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.

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回答（1 个）

Torsten
Torsten 2016-11-9
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.

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