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01af
Posts:
2
Registered:
1/7/13


system of differential equations mathematica help
Posted:
Jan 7, 2013 11:05 PM


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 nonnumerical 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. thanks in advance a.



