       Non-linear Boundary Diff equations

• To: mathgroup at smc.vnet.net
• Subject: [mg32128] Non-linear Boundary Diff equations
• From: Sim Sze Kuan <sszekuan at dso.org.sg>
• Date: Fri, 28 Dec 2001 02:41:46 -0500 (EST)
• Organization: DSO National Laboratories
• Sender: owner-wri-mathgroup at wolfram.com

```I have a system of non-linear coupled first order differential
equations:

d A(t)/dt = -2.12A(t) - 0.004487{C(t) + D(t)}A(t)
d B(t)/dt = +2.12B(t) +0.004487{C(t) + D(t)}B(t)
d C(t)/dt = -1.75C(t) +0.00472{A(t) + B(t)}C(t)
d D(t)/dt = +1.75D(t) -0.00472{A(t) + B(t)}D(t)

with boundary conditions A(0)=any +ve number (say 100), B(5)=0.9A(5),
C(0)=0.9D(0), D(5)=0.9C(5)

It is natural to use NDSolve[{equations,boundary conditions, {A, B,C,D},
{t,0,5}] and solve the problem numerically. Specifically, my problem
apparently comes from the boundary conditions used. It seems that I have
to set all the boundary conditions for ABCD at the same point t (say
t=0, then boundary conditions are A(0)=...,B(0)=..,C(0)=...,D(0)...),
otherwise if for what my problem required, I set the boundary conditions
for function A,C at t=0 and functions B,D at t=5, I get the meassage:

NDSolve:: ndv : For a boundary value problem, only nth order single
linear ordinary differential equations is supported.........

It seems to me that the problem is not peculiar to my system of
equations, other relatively simpler systems of equations may faced the
same problems when boundary conditions at diffrent points have to be
used.

Does anyone has an alternative solution to this or can anyone explained
the reason or provide some relevant advise. Thankyou and wish you a
Happy New Year.

```

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