solve a complex second order differential equation

17 views (last 30 days)
the ode has a form:
and for, given , how could I use ode45 to solve it with plot? thx

Accepted Answer

Bjorn Gustavsson
Bjorn Gustavsson on 20 Oct 2021
Edited: Bjorn Gustavsson on 20 Oct 2021
The first step is to convert your second-order ODE to two coupled first-order ODEs:
Then you should write that ODE-system as a matlab-function:
function [dphidt_domegadt] = yourODEs(t,phi_w)
phi = phi_w(1);
w = phi_w(2);
dphidt = w;
if t == 0 % Here I assume that domegadt/t goes to zero as t -> 0+, perhaps there are solutions for other finite values of that ratio...
domegadt = phi^3;
domegadt = -2/t*dphidt - phi^3;
dphidt_domegadt = [dphidt;
This should be possible to integrate with ode45:
phi0w0 = [1 0];
t_span = [0 exp(2)]; % some limits of yours
[t,phi_w] = ode45(@(t,phi_w) yourODEs(t,phi_w),t_span,phi0w0);
嘉杰 程
嘉杰 程 on 22 Oct 2021
actually this is only a specific function when n=3

Sign in to comment.

More Answers (1)

Walter Roberson
Walter Roberson on 20 Oct 2021
You cannot use any numeric solver for that. You have initial conditions at η = 0, but at 0 you have a division by 0 which gets you a numeric infinity. That numeric infinity is multiplied by the boundary condition of 0, but numeric infinity times numeric 0 gives you NaN, not 0.
If you work symbolically you might think that the infinity and the 0 cancel out, but that only works if the φ' approaches 0 faster than 1/η approaches infinity, which is something that we do not immediately know to be true.





Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!