Problem with Mathematica

Question

Lazaros Moysis 2012-6-13

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/41113-problem-with-mathematica

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

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Walter Roberson 2012-6-13

This resource is _entirely_ about MATLAB . Maple is sometimes discussed here because Maple was previously used for the MATLAB Symbolic toolbox.

I will try your system out in Maple later tonight when I get home, but it will be several hours.

Andreas Goser 2012-6-14

As an anecdote: I remember when I was doing technical and installation support myself, customers called us for other products sometimes and when we suggested to call the vendor, the customers (who also used MATLAB for some applications) said: "Yes, I know, but your service is much better" :-)

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Answer 1

Walter Roberson 2012-6-14

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/41113-problem-with-mathematica#answer_50699

在 MATLAB Online 中打开

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.