Question on PDE
- To: mathgroup at smc.vnet.net
- Subject: [mg48696] Question on PDE
- From: Lautaro Vergara <lvergara at lauca.usach.cl>
- Date: Thu, 10 Jun 2004 02:44:50 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear people,
I need to automatize a problem like the one shown below. I'll appreciate
very much any comments to this respect.
Let the following PDE that depends on two parameters, a and b
In[337]:=
\!\(s1 := NDSolve[{
2\ Pi\ \((t^2 +
V1[x, t])\)\ D[U[x, t], t] + V2[x, t,a] \[Equal] 0, U[x,
t0] \[Equal] \((\(-x\) + 4\
lambda\ x^3)\)\ \[ExponentialE]\^\(\(-a\)\ x\^2\),
U[0, t] \[Equal] 0,
U[b, t] \[Equal] 0}, U, {x, 0, b}, {t, t0, tf}]\)
where
In[334]:=
t0=500;tf=0.0;lambda=0.06;
In[335]:=
V1[x_,t_]:=Exp[a x^2] (2 a x U[x,t]+D[U[x,t],x])
In[336]:=
\!\(V2[x_, t_] := \((2\ a\ \((1 + 2\
a\ x\^2)\)\ U[x, t] + 4\ a\ x\ D[U[x, t], x] + D[D[U[x, t], x],
x])\)\)
I need to evaluate the following function and found the values of a and
b that makes this function independent of them
In[338]:=
s2a[x_,t_]:=Exp[a x^2] U[x,t]/.s1[[1]]
I have done by hand by making a DO of the variable a and then playing
with different values of b such that what is looked for happens.
Do you know a way of doing this more efficiently?
Thanks in advance,
Lautaro