NDSolve cannot solve set of ODEs
in [Mathematica]
|
From: Zachar István on 22 Apr 2010 03:31 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}]
From: Alois Steindl on 22 Apr 2010 06:43 Hello, your ODE for v contains a V[t] instead of v[t]. Quite hard to spot. Good luck Alois
From: István Zachar on 22 Apr 2010 06:44 Thank you Alois and Simon for your typo-hunt, I've checked it thoroughly (obviously not that thoroughly) for two days, and could not spot it : ) It indeed works now. Istvan On 4/22/2010 10:31 AM, Alois Steindl wrote: > Hello, > your ODE for v contains a V[t] instead of v[t]. > Quite hard to spot. > > Good luck > Alois >
From: Simon Pearce on 22 Apr 2010 06:44 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(a)gmail.com] Sent: 22 April 2010 08:32 Subject: 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}] = This message has been checked for viruses but the contents of an attach= ment=0D=0Amay still contain software viruses which could damage your co= mputer system:=0D=0Ayou are advised to perform your own checks. Email c= ommunications with the=0D=0AUniversity of Nottingham may be monitored a= s permitted by UK legislation.=
From: Bob Hanlon on 23 Apr 2010 03:51 I recommend that you define your equation and variable lists outside the NDSolve and check with Complement[Cases[eqns, x_Symbol[t] -> x, Infinity] // Union, vars] Bob Hanlon ---- "Istv=C3=A1n Zachar" <replicatorzed(a)gmail.com> wrote: ========================== Thank you Alois and Simon for your typo-hunt, I've checked it thoroughly (obviously not that thoroughly) for two days, and could not spot it : ) It indeed works now. Istvan On 4/22/2010 10:31 AM, Alois Steindl wrote: > Hello, > your ODE for v contains a V[t] instead of v[t]. > Quite hard to spot. > > Good luck > Alois >
|
Pages: 1 Prev: Line changes length in animation Next: Imposing constraints on a system of equations |