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Numerical solution of coupled nonlinear PDEs
*To*: mathgroup at smc.vnet.net
*Subject*: [mg112092] Numerical solution of coupled nonlinear PDEs
*From*: "Dominic" <miliotodc at rtconline.com>
*Date*: Mon, 30 Aug 2010 06:19:16 -0400 (EDT)
Hi guys,
For the functions a(t,y), b(t,y), and x(t,y),I have the PDE system:
a'=a''+a x''+x'a'
b'=b''-bx''-x'b'
x''=b-a
Sorry I can't show the system more clearly here but on the left side the
partial is respect to t for a and b and it's with respect to y for the
x(t,y), and on the right, all partials are with respect to y,
and I'd like to obtain a numerical solution for any simple IBVP using
NDSolve, for example in the domain 0<t<1 and 0<y<1 with all initial
conditions set to y This is the code I'm using:
mysol = NDSolve[{D[a[t, y], t] ==
D[a[t, y], {y, 2}] + a[t, y] D[x[t, y], {y, 2}] +
D[x[t, y], y] D[a[t, y], y]
,
D[b[t, y], t] ==
D[b[t, y], {y, 2}] - b[t, y] D[x[t, y], {y, 2}] -
D[x[t, y], y] D[b[t, y], y]
,
D[x[t, y], {y, 2}] == b[t, y] - a[t, y]
,
a[0, y] == y, a[t, 0] == 0, a[t, 1] == 1,
b[0, y] == y, b[t, 0] == 0, b[t, 1] == 1,
x[0, y] == y, x[t, 0] == 0, x[t, 1] == 1},
{a, b, x}, {t, 0, 1}, {y, 0, 1}, MaxSteps -> 10000]
However, I receive boundary-value errors and singular errors.
Can someone help me set up this system in any way for any reasonable
domain with any reasonable initial and bondary values to obtain a
non-trivial solution?
Thanks guys,
Dominic
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