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