```Date: Jan 8, 2013 11:39 PM
Author: Oliver Ruebenkoenig
Subject: Re: system of differential equations mathematica help

On Mon, 7 Jan 2013, 01af wrote:> 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.> thanks in advance> a.>>Hi 01af,to be quite honest I did not see what the issue was and had to resort asking colleagues myself. What you can do is: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},  Method -> {"BoundaryValues" -> {"Shooting",      "StartingInitialConditions" -> {a[0] == 1, a'[0] == 0, p[0] == 0,         u[0] == .1}}}]The issue is that the default starting conditions produce singularities - so I filed this as a suggestion for future improvement that in such a case other starting conditions are attempted.Hope this helps,Oliver
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