Help wanted with using NDSolve

Question

Parameters

gamma = 7.16*10^-12;
mu = 2.15*10^-3;
kappa = 28.55*10^-5;
rho = 1.80*10^3;

The system of the differential equations

 soln1 = 
   NDSolve[
     {(mu + kappa) u''[r] + u'[r]/r - 2 kappa w'[r] == 0, 
      gamma w''[r] + w'[r]/r + 2 kappa u'[r] + u[r]/r - 4 kappa w[r] == 0,
      p'[r] == rho u[r]^2 /2, 
      u[0] == 0, u[1] == 1, w[0] == 0, w[1] == 1, p[0] == 0}, 
     {u, w, p}, {r, 0, 1}];`

Plotting

u = u[r] /. soln1;
w = w[r] /. soln1;
p = p[r] /. soln1;
Plot[{u}, {r, 0, 1}, 
  LabelStyle -> 20, 
  Frame -> True, 
  FrameLabel -> {{" u", "  "}, {" r", " "}}, 
  PlotStyle -> Black]

when I run it I face with this error: $RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of u[r]. — sajad.sharhani, Jun 14 '17 at 14:36
I don't know if it's the only problem but I guess you should write p[0]==0 — Valacar, Jun 14 '17 at 14:38
when I run it face with this error: $RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of u[r]. — sajad.sharhani, Jun 14 '17 at 14:38
Possible duplicate of Solving a second-order nonlinear differential equation — zhk, Jun 14 '17 at 16:54
I get a completely different error, which makes this unclear what your problem is. Please verify in a clean session that the posted code actually does what you claim. I'd assume you get a successful solution to NDSolve otherwise why bother trying to plot..? — george2079, Jun 14 '17 at 21:42

score 0 · Accepted Answer · answered Jun 14 '17 at 23:02

You have two problems.

Your system of ODE is ill posed and can not be solved.
Your code for extracting the solutions for plotting is bad. The recursion errors you are getting come from trying to assign solutions to the variable names you used in the system.

Assuming you correct your equations and boundary values so that you actually get a solution, you can safely extract the interpolating functions representing the solution and plot them as follows:

{uF, wF, pF} = soln1[[1, All, 2]];
Plot[[{uF[r], wF[r], pF[r]}, {r, 0, 1}]

Help wanted with using NDSolve

1 Answers1