Re: NDSolve (loop)

• To: mathgroup at smc.vnet.net
• Subject: [mg116996] Re: NDSolve (loop)
• From: greg28 <grega.smrkolj at gmail.com>
• Date: Mon, 7 Mar 2011 05:47:03 -0500 (EST)

```Hi,
let me be more specific about my problem. My code in mathematica is:

_______________________________________
T=1000 (truncation of time, assuming that V(s,x)-> V(x)
as T-> infinity)

alpha= 0.1
pde= some complicated expression (involving 1st and 2nd
order derivatives)

soln = NDSolve[{pde, V[0, x] == 0,
V[s, xu] == 0, (D[V[s, x], x] /. x -> xd) == 0},
V[s, x], {s, 0, T}, {x, xd, xu},
Method -> {"MethodOfLines",
"SpatialDiscretization" -> {"TensorProductGrid",
"MinPoints" -> 1000}} ]
_______________________________________

This is then a particular solution for alpha=0.1.
However, my problem is to find a value of alpha,
at which, for instance, V[x=0.3]=alpha/2. So I
need to write a loop which will stop when this
condition is satisfied. The problem is that one
evaluation takes a lot of time, so I wonder whether
it is somehow possible to speed up NDSolve, e.g.
by somehow telling mathematica what the solution for
alpha=0.1 was when solving for alpha=0.2 or something
like this. The shape of V should not differ too much
between alpha=0.1 and alpha=0.2...

```

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