system of differential equations mathematica help

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• Subject: [mg129366] system of differential equations mathematica help
• From: 01af <alicerferrier at gmail.com>
• Date: Mon, 7 Jan 2013 23:07:41 -0500 (EST)
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```Before anyone starts to type: I have read the top post on a similar matter, but the reply makes no sense to me so if anyone can give my issue a read through I would be grateful. Thanks.

ok I am modelling airflow in the upper airway for application i obstructive sleep apnoea, but I have hit a brick wall with mathematica. I have a system of 3 differential equations with boundary conditions, and I need to solve to find 3 unknown functions numerically so that they may be plotted in various graphs.

The equations are as follows:

D[a[x]*u[x], x] == 0,
u[x] u'[x] == -p'[x],
p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]).

with boundary conditions:

u[0] == 0.1, a[0] == 1, a[10] == 1, p[10] == 1.

so initially I tried to use NDSolve like so..

Code:

NDSolve[{D[a[x]*u[x], x] == 0, u[x] u'[x] == -p'[x],
p[x] - 1 == 2 (1 - ((a[x])^(-3/2))) - 50 (a''[x]), u[0] == 0.1,
a[0] == 1, a[10] == 1, p[10] == 1}, {a}, {x, 0, 10}]

but mathematica does this:

Code:

Power::infy: "Infinite expression 1/0.^(3/2) encountered. "
Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >>
Infinity::indet: Indeterminate expression 0. ComplexInfinity encountered. >>
General::stop: Further output of Infinity::indet will be suppressed during this calculation. >>
NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.`. >>

which is super annoying, any pointers as to where I'm going wrong would be great. I'm not even sure if I should be using NDSolve so let me know what you think.