Finding Blowup of an ODE with maple

Question

I've been interested in finite blowups of odes lately. I'm looking for a good way to calculate blowup times in maple. Right now all I do is to use dsolve, plot the ode, and then look where the solution appears to blowup. Unfortunately, this is rather cumbersome for my computer to handle for the odes I'm interested in. Just wondering if someone knew of another way to calculate the blowup times. I can use other math programs as well, I'm just most comfortable with maple. Thanks in advance for your help.

Answer 1

At least in Maple 16, dsolve tells me about singularity explicitly, without me having to look at the graph. For example:

IVP:=[diff(w(t),t$4)+w(t)^3=0, w(0)=0, D(w)(0)=0, (D@@2)(w)(0)=0, (D@@3)(w)(0)=1];
dsolve(IVP, w(t), numeric,  range=0..6);

Result:

Warning, cannot evaluate the solution further right of 5.5472807, probably a singularity.

Or, for the equation you were originally interested in:

IVP:=[diff(w(t),t$4)+diff(w(t),t$2)+w(t)^3=0, w(0)=0, D(w)(0)=0, (D@@2)(w)(0)=0, (D@@3)(w)(0)=1];
dsolve(IVP, w(t), numeric,  range=0..7);

Result:

Warning, cannot evaluate the solution further right of 6.2805222, probably a singularity

Hm, that looks suspiciously close to $2\pi$...

Answer 2

Have you tried matlab? I calculate the follows: dsolve('D4y+D2y+y^3=0','y(0)=0','Dy(0)=1','D2y(0)=0','D3y(0)=0')

I also have tried sevral ICs, but it said there is no solutions. Also ODE23 ODE45 can be used. Good luck.