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OK guys, here's the thing, mathematica does not return a solution for this system of dif.equations

DSolve[{p11'[t] == 2*p12[t] - (1/r)*p12[t]^2,

p12'[t] ==

p22[t] - (w^2)*p11[t] - 2*z*w*p12[t] - (1/r)*p12[t]*p22[t],

p22'[t] == -2*(w^2)*p12[t] -

4*z*w*p22[t] - (1/r)*p22[t]^2 + (w^4)*q, p11[0] == 0, p12[0] == 0,

p22[0] == 0}, {p11[t], p12[t], p22[t]}, t]

Can anyone please try it on your system and tell me if u have the same problem?

i Also tried with the NDSolve function

NDSolve[{p11'[t] == 2*p12[t] - (1/r)*p12[t]^2,

p12'[t] ==

p22[t] - (w^2)*p11[t] - 2*z*w*p12[t] - (1/r)*p12[t]*p22[t],

p22'[t] == -2*(w^2)*p12[t] -

4*z*w*p22[t] - (1/r)*p22[t]^2 + (w^4)*q, p11[0] == 0, p12[0] == 0,

p22[0] == 0}, {p11[t], p12[t], p22[t]}, {t, 0, 10}]

but i get the error message:NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`

I greatly appreciate your help

Laz.

(i use mathematica 8.0)

I know this is mostly about matlab questions, but i hope that should be no problem

Andreas Goser
on 14 Jun 2012

Walter Roberson
on 14 Jun 2012

In Maple, the expression would be

dsolve([diff(p11(t), t) = 2*p12(t)-p12(t)^2/r, diff(p12(t), t) = p22(t)-w^2*p11(t)-2*z*w*p12(t)-p12(t)*p22(t)/r, diff(p22(t), t) = -2*w^2*p12(t)-4*z*w*p22(t)-p22(t)^2/r+w^4*q, p12(0) = 0, p11(0)=0, p22(0)=0])

Maple says this has no solution.

If you reduce the initial conditions to p12(0)=0 and leave p11(0) and p22(0) undetermined, then the system has two solutions,

p11(t) = (-2*z*r+(4*r^2*z^2+w^2*q*r)^(1/2))/w

p12(t) = 0

p22(t) = w*(-2*z*r+(4*r^2*z^2+w^2*q*r)^(1/2))

and

p11(t) = -(2*z*r+(4*r^2*z^2+w^2*q*r)^(1/2))/w

p12(t) = 0

p22(t) = -w*(2*z*r+(4*r^2*z^2+w^2*q*r)^(1/2))}

(The two are similar but have some sign changes.)

If one examines these solutions then one would note that these are independent of t, so if one imposes that p11(0)=0 then that implies that p11(t) and p22(t) must all be 0 (not impossible given the formula but it requires r=0 or requires some peculiar w and q relationships)

There is also a solution for the equations without the initial value conditions if p12(t) = 2*r.

There is a third solution for the equations without the initial value conditions that is fairly complex and appears to be defined recursively. I do not understand what Maple is trying to say in its output. In any case it is clear from what I do understand that the combination {p11(0)=0, p12(0)=0, p22(0)=0} as initial conditions has no solution for the set of equations.

Walter Roberson
on 14 Jun 2012

I used Maple, not Mathematica. (I think back when I was using Mathematica, it was Mathematica 2 !)

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