MATLAB: ODE with a cubic root, ODE45 can’t solve

nonlinearode45

Im trying to solve the following ODE, with has a peculair cubic-root as a nonlinearity (p). If this nonlinearity is uneven natural number, this is solved within a second.
But for the cubic root case, the solver doesn't seem to able to solve this. I've added a progress bar ( text-progress-bar-for-odes ) but it seems to be stuck at 0 %. Maybe the infinite derivative of x^1/3 at the origin is the problem.
Does anybody know how to get this simulation working? Thanks.
m = 1;
k = 1;
c = 0.000;
omega0 = sqrt(k/m);
x0_dot = 0.1;
Tl = 20;
%%NES
mna =0.02;
cna = 0.002;
kna = 0.4444;
p = 1/3;
 f1 = @(t,y)[y(3);y(4);...
    -(k*y(1) + c*y(3)+ kna*(y(1)-y(2))^p+cna*(y(3)-y(4)))/m;...
    -(kna*(y(2)-y(1))^p + cna*(y(4)-y(3)))/mna;...
    ];
Prec = 1e-14;
options = odeset('RelTol',Prec,'AbsTol',[Prec Prec Prec Prec],'OutputFcn',@odetpbar);
[T1,Y1] = ode45(f1,[0 Tl],[0 0 x0_dot 0],options);

Best Answer

Instead of x^p, write sign(x)*(abs(x))^p.
Best wishes
Torsten.
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