Hello,

I have a problem in the solution of this system of ODEs:

de[1] := M*(diff(x(t), t, t))+sum(FxjR, j = 1 .. m)+sum(FxjL, j = 1 .. m) = M*g+Us*omIn^2*cos(omIn*t); ini[1] := x(10^(-6)) = 1.00013081730872*10^(-6); ini[2] := (D(x))(10^(-6)) = 0.261632327671976e-3;

de[2] := M*(diff(y(t), t, t))+sum(FyjR, j = 1 .. m)+sum(FyjL, j = 1 .. m) = Us*omIn^2*sin(omIn*t); ini[3] := y(10^(-6)) = 9.99989124246935*10^(-8); ini[4] := (D(y))(10^(-6)) = -2.50318090194868*10^(-6);

de[3] := M*(diff(z(t), t, t))+sum(FzjR, j = 1 .. m)+sum(FzjL, j = 1 .. m) = 0; ini[5] := z(10^(-6)) = 9.99065455347471*10^(-9); ini[6] := (D(z))(10^(-6)) = -0.186933812655399e-4;

de[4] := Ix*(diff(thx(t), t, t))+Iz*(diff(thy(t), t))*omIn+sum(MxjL, j = 1 .. m)-sum(MxjR, j = 1 .. m) = 0; ini[7] := thx(10^(-6)) = 8.60546055625759*10^(-7); ini[8] := (D(thx))(10^(-6)) = 1.72109307183424;

de[5] := Iy*(diff(thy(t), t, t))-Iz*(diff(thx(t), t))*omIn+sum(MyjL, j = 1 .. m)-sum(MyjR, j = 1 .. m) = 0; ini[9] := thy(10^(-6)) = 1.02142988540396*10^(-10); ini[10] := (D(thy))(10^(-6)) = 0.285764338010142e-3;
 

sys_ode := seq(de[n], n = 1 .. 5);
ICs := seq(ini[n], n = 1 .. 10);
F := dsolve([sys_ode, ICs], type = numeric, range = 10^(-6) .. 0.1);
 

Then I found this response:

Warning, cannot evaluate the solution further right of .10473416e-4, probably a singularity
F:=proc(x_rkf45) ... end proc

The details of the parameters inside the SUMMATION sign are very complicated and it is useless to mention them (in my point of view). Each one of (FxjR) and its similars is more than 20 Word pages, so it is useless to mention, but I can confirm that all of them include the (time and the 5 variables of ODE and their first derivatives only).

How can I solve that?
Any ideas to get rid of this singularity problem?

I am thinking of using a fixed step method, but I do not know if this will solve the problem? Also, I do not know how can I use a fixed step and what are the methods that use fixed step in maple?

Your participations are greatly appreciated! 

I have a system of nonlinear ODE and I solved them numerically using rkf45. the solution is in time domain and the variables are x, y and z.

I want to convert this solution from time domain to frequency domain. I know that I should do FFT, but I do not know how to do this. 

I tried to do this, but I found that I have to get the solution of x, y and z in the form of vector with respect to time. I am not sure if I understant this problem corectly.

Thanks in advance.