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?