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Question: Solving a set of ODE's

Question:Solving a set of ODE's

Benj 52 Maple
solve ode dsolve numeric
August 16 2011
0

I'm currently trying to solve a set of ODE's using dsolve/numeric and I'm unsure about the result I'm getting.  Some help with the worksheet and general help with the solution method would be appreciated.

 

Here are the equations:

 diff(b1(t), t) = I*u1(t)

diff(b2(t), t) = I*u2(t)-3*b1(t)/(2*omega)

diff(b3(t), t) = I*u3(t)

diff(u1(t), t) = I*b1(t)+2*u2(t)/omega-gradQ1

diff(u2(t),t)=I*b2(t)-1/(2*omega)*u1(t) - gradQ2

diff(u3(t), t) = I*b3(t)+I*b3(t)-gradQ3

Where ω and κ are parameters (nominally, I can set them to 0.125 but would like to be able to change them around later).

gradQ is defined as:

gradQ2 = (3*K*u2(t)-2*u1(t)*omega)/((9/4)*K+omega^2+omega^2/kappa^2)

gradQ1 = 1.5 * K * gradQ2/ω

gradQ3 = gradQ2/κ

and K = (x + t) 

 

The initial conditions are:

b1(0) = exp(-(1/25)*ln(2)*x^2), b2(0) = (3/25*I/ω)*ln(2)*x*exp(-(1/25)*ln(2)*x^2), b3(0) = 0, u1(0) = 0, u2(0) = 0, u3(0) = 0

I would like to integrate these equations from x = -64..64 and from t=0..16

The command I've been using is dsolve passed with the numeric and parameters=[x] options.

 

Again, any help is much appreciated.
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