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Re: NDSolve cannot solve set of ODEs

• To: mathgroup at smc.vnet.net
• Subject: [mg109345] Re: NDSolve cannot solve set of ODEs
• From: Simon Pearce <Simon.Pearce at nottingham.ac.uk>
• Date: Thu, 22 Apr 2010 06:44:13 -0400 (EDT)
• References: <201004220732.DAA09749@smc.vnet.net>

You have a capital V[t] in the equation for v'[t], changing this to v[t] =
gives an answer.

Simon

-----Original Message-----
From: Zachar Istv=E1n [mailto:replicatorzed at gmail.com]
Sent: 22 April 2010 08:32
To: mathgroup at smc.vnet.net
Subject: [mg109345] [mg109338] NDSolve cannot solve set of ODEs

Dear group,

I have a set of ODequations (see below, the ordinary Chemoton modell),
which when evaluated, returns the following error:

NDSolve::ndnum: Encountered non-numerical value for a derivative at t
== 0.`. >>

Could you please pinpoint any mistake here? Thanks in advance.\
Istvan



NDSolve[{

\!\(\*SuperscriptBox["x", "\[Prime]",
MultilineFunction->None]\)[t] == 1,

\!\(\*SuperscriptBox["y", "\[Prime]",
MultilineFunction->None]\)[t] == 1,

\!\(\*SuperscriptBox["a1", "\[Prime]",
MultilineFunction->None]\)[t] ==
   a2[t] + 2 (-a1[t]^2 + a5[t]) - a1[t]*x[t],

\!\(\*SuperscriptBox["a2", "\[Prime]",
MultilineFunction->None]\)[t] == -2 a2[t] + a1[t]*x[t] + a3[t]*y[t],

\!\(\*SuperscriptBox["a3", "\[Prime]",
MultilineFunction->None]\)[t] ==
   a2[t] - a3[t] + a4[t]*v[t] - a3[t]*y[t],

\!\(\*SuperscriptBox["a4", "\[Prime]",
MultilineFunction->None]\)[t] ==
   a3[t] - a4[t] + a5[t]*tp[t] - a4[t]*v[t],

\!\(\*SuperscriptBox["a5", "\[Prime]",
MultilineFunction->None]\)[t] == a1[t]^2 + a4[t] - a5[t] -
a5[t]*tp[t],

\!\(\*SuperscriptBox["v", "\[Prime]",
MultilineFunction->None]\)[t] ==
   a3[t] + pV1[t]*r[t] - pV0[t]*V[t] - a4[t]*v[t] - pV1[t]*v[t] -
    pV2[t]*v[t] - pV3[t]*v[t] - pV4[t]*v[t] - pV5[t]*v[t],

\!\(\*SuperscriptBox["r", "\[Prime]",
MultilineFunction->None]\)[t] == -pV1[t]*r[t] + tm[t] - ts[t] -
    r[t]*ts[t] + pV0[t]*v[t] + pV1[t]*v[t] + pV2[t]*v[t] +
    pV3[t]*v[t] + pV4[t]*v[t] + pV5[t]*v[t],

\!\(\*SuperscriptBox["tp", "\[Prime]",
MultilineFunction->None]\)[t] == a4[t] - tp[t] - a5[t]*tp[t],

\!\(\*SuperscriptBox["ts", "\[Prime]",
MultilineFunction->None]\)[t] == tm[t] + tp[t] - ts[t],

\!\(\*SuperscriptBox["tm", "\[Prime]",
MultilineFunction->None]\)[t] == -tm[t] - s[t]*tm[t] + r[t]*ts[t],

\!\(\*SuperscriptBox["pV0", "\[Prime]",
MultilineFunction->None]\)[t] ==
   pV1[t]*r[t] - pV0[t]*v[t] + 2*pV5[t]*v[t],

\!\(\*SuperscriptBox["pV1", "\[Prime]",
MultilineFunction->None]\)[t] == -pV1[t]*r[t] + pV0[t]*v[t] -
    pV1[t]*v[t],

\!\(\*SuperscriptBox["pV2", "\[Prime]",
MultilineFunction->None]\)[t] == -pV2[t]*r[t] + pV1[t]*v[t],

\!\(\*SuperscriptBox["pV3", "\[Prime]",
MultilineFunction->None]\)[t] == -pV3[t]*r[t] + pV2[t]*v[t],

\!\(\*SuperscriptBox["pV4", "\[Prime]",
MultilineFunction->None]\)[t] == -pV4[t]*r[t] + pV3[t]*v[t],

\!\(\*SuperscriptBox["pV5", "\[Prime]",
MultilineFunction->None]\)[t] == -pV5[t]*r[t] + pV4[t]*v[t],

\!\(\*SuperscriptBox["s", "\[Prime]",
MultilineFunction->None]\)[t] == s[t]*tm[t],

\!\(\*SuperscriptBox["q", "\[Prime]",
MultilineFunction->None]\)[t] == s[t]^(3/2.),

  x[0] == 0.4, y[0] == 0,
  a1[0] == 0.4, a2[0] == 0, a3[0] == 0, a4[0] == 0, =
a5[0] == 0,
  v[0] == 0.01, r[0] == 0.01, tp[0] == 0.01, ts[0] == 0, =
tm[0] == 0,
  pV0[0] == 0.01, pV1[0] == 0, pV2[0] == 0, pV3[0] == 0, =
pV4[0] == 0,
  pV5[0] == 0,
  s[0] == 0.2, q[0] == 1},

 {x, y, a1, a2, a3, a4, a5, v, r, tp, ts, tm, pV0, pV1, pV2, pV3, pV4,
   pV5, s, q}, {t, 0, 10}]

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• References:
  • NDSolve cannot solve set of ODEs
    • From: Zachar István <replicatorzed@gmail.com>