# Question:Probably a singularity in system of ODE

## Question:Probably a singularity in system of ODE

Maple

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!

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