MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

NDSolve: Distinguishing equations


I have a set of three PDEs that I want to solve using NDSolve (in
Mathematica 4).  Unfortunately I seem to keep getting two errors.  One is
that there are no intial values specified (even though there are enough for
me to solve it exactly, which I have already done).  So if I add more
initial values, I get a message stating ""a clear distinction cannot be
found between the PDE's, initial values, and boundary conditions."

So is there some general order or rules for the equations I give NDSolve to
solve to avoid the chances of this second error?

For more specifics, below are the three equations, (some constant setting,)
and the NDSolve commands and errors.  My goal is to add a non-linear term
to these equations and solve them, but first I want to understand NDSolve
enough to get this to work.  Thanks for any help.

In[1]:= eq1 = \[Rho] D[v[y, t], t] == D[\[Sigma][y, t], y]

In[2]:= \!\(eq2 = 
    D[\[Sigma][y, t], 
        t]\  == \ \[Mu]\ D[v[y, t], 
            y] - \(\(2\ \[Mu]\)\/\[Tau]\) \((\[Lambda]\ \[Sigma][y, 
                  t] - \[CapitalDelta][y, t])\)\)

In[3]:= \!\(eq3 = 
    D[\[CapitalDelta][y, t], 
        t] == \(1\/\[Tau]\) \((\[Lambda]\ \[Sigma][y, t] -
\[CapitalDelta][y, 
              t])\)\)

In[4]:= \[Rho] = 1; \[Mu] = 1; \[Lambda] = 1; \[Tau] = 1; h = 1;

In[5]:= \[Omega] = \[Pi]/15;

In[6]:= \!\(\(\[Epsilon]\_m =  .01;\)\)

In[7]:= Clear[\[Sigma], \[CapitalDelta], v]

In[8]:= \!\(NDSolve[{eq1, eq2, eq3, v[0, t] == \(-v[h, t]\), 
      v[0, t] == \(1\/2\) h\ \[Epsilon]\_m\ \[Omega]\ E\^\(I\ \[Omega]\
t\), 
      v[0, 0] == \(1\/2\) 
          h\ \[Epsilon]\_m\ \[Omega]}, {\[Sigma], \[CapitalDelta], v}, {y,
0, 
      h}, {t, 0, 10*2  \[Pi]/\[Omega]}]\)

NDSolve::"ivnone": "No initial values specified."

In[9]:= \!\(NDSolve[{eq1, eq2, eq3, 
      v[0, t] == \(1\/2\) h\ \[Epsilon]\_m\ \[Omega]\ E\^\(I\ \[Omega]\
t\), 
      v[h, t] == \(-\(1\/2\)\) 
          h\ \[Epsilon]\_m\ \[Omega]\ E\^\(I\ \[Omega]\ t\), 
      v[0, 0] == \(1\/2\) h\ \[Epsilon]\_m\ \[Omega], \[Sigma][y, 0] == 
        0, \[CapitalDelta][y, 0] == 0}, {\[Sigma], \[CapitalDelta], v}, {y, 
      0, h}, {t, 0, 10*2  \[Pi]/\[Omega]}]\)

\!\(\*
  RowBox[{\(NDSolve::"pdivbc"\), \(\(:\)\(\ \)\), "\<\"In
\\!\\({\\(\\(\\(\\(\
\\(\\(\\*SuperscriptBox[\\\"v\\\", TagBox[\\((0, 1)\\), Derivative], \
Rule[MultilineFunction, None]]\\)\\)[\\(\\(y, t\\)\\)]\\)\\) == \
\\(\\(\\(\\(\\*SuperscriptBox[\\\"\[Sigma]\\\", TagBox[\\((1, 0)\\), \
Derivative], Rule[MultilineFunction, None]]\\)\\)[\\(\\(y, \
t\\)\\)]\\)\\)\\)\\), \\(\\(\[LeftSkeleton] 6 \[RightSkeleton]\\)\\), \
\\(\\(\\(\\(\[CapitalDelta][\\(\\(y, 0\\)\\)]\\)\\) == 0\\)\\)}\\), a clear
\
distinction cannot be found between the PDE's, initial values, and boundary
\
conditions.\"\>"}]\)


  • Prev by Date: Re: NDSolve
  • Next by Date: Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
  • Previous by thread: ConstrainedMin and vector-notation
  • Next by thread: Re: Problem with evaluation of delayed rules(addendum)