Re: solve errors...
- To: mathgroup at smc.vnet.net
- Subject: [mg43071] Re: solve errors...
- From: sean kim <shawn_s_kim at yahoo.com>
- Date: Sun, 10 Aug 2003 01:46:58 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
appears that is an artifact of the yahoo email thing. yahoo seems to
have put a line where the space is mising between k's and variables...
the original i have is ok though.
and that's what was used to solving for the variables.
thank you.
--- wouter meeussen <wouter.meeussen at pandora.be> wrote:
> dear Sean,
>
> watch those typo's:
> Your Out[38] contains
> Derivative[1][k][t] == k11*h[t]*i[t] - k12*k[t] - k13*d[t]*k[t] +
> k14l[t],
> ...
> and "k14l[t] " should be "k14 * l[t]"
> same for
> Derivative[1][o][t] ==
> k18*m[t]*n[t] - k19*o[t] - k20*o[t]*p[t] + k21q[t],
>
> and, personally I would replace function "t[t]" with "tt[ t ]" for
> clarity.
>
> Success,
>
> Wouter.
>
> ----- Original Message -----
> From: "sean kim" <shawn_s_kim at yahoo.com>
To: mathgroup at smc.vnet.net
> Newsgroups: comp.soft-sys.math.mathematica
> Sent: Saturday, August 09, 2003 9:13 AM
> Subject: [mg43071] solve errors...
>
>
> > Hello Group.
> >
> > I don't know if this question has been adressed in the past... If
> there
> > was a post about it, I haven't been able to locate it.
> >
> > here's the problem.
> >
> > Please consider the following reduced steady state system which is
> > generated from a larger ODE system. with some assumptions, the
> larger
> > system reduces down to below. ( original system is posted at the
> end of
> > the message)
> >
> > { 0 == -k23 n[t] s[t] + k24 t[t],
> > 0 == k23 n[t] s[t] - k24 t[t],
> > 0 == -k11 h[t] i[t] + k12 k[t],
> > 0 == k11 h[t] i[t] - k12 k[t],
> > 0 == -k16 e[t] - k28 e[t] i[t] + k17 w[t] + k29 x[t],
> > 0 == k16 e[t] - k17 w[t],
> > 0 == k28 e[t] i[t] - k29 x[t] - k30 x[t],
> > 0 == -k23 n[t] s[t] + k24 t[t],
> > 0 == -k28 e[t] i[t] - k11 h[t] i[t] + k12 k[t] + k29 x[t] + k30
> > x[t]}
> >
> > as far as i understand it, given a number of algebraic equations,
> with
> > equal number of variables, then the system should be solvable in
> terms
> > of the variables. Am I not correct?
> >
> > there are 9 equations and 9 variables in this system, shouldn't it
> > render itself to solution? it appears it isn't.
> >
> > In[36]:=
> > Solve[{0 == -k23 n[t] s[t] + k24 t[t],
> > 0 == k23 n[t] s[t] - k24 t[t],
> > 0 == -k11 h[t] i[t] + k12 k[t],
> > 0 == k11 h[t] i[t] - k12 k[t],
> > 0 == -k16 e[t] - k28 e[t] i[t] + k17 w[t] + k29 x[t],
> > 0 == k16 e[t] - k17 w[t],
> > 0 == k28 e[t] i[t] - k29 x[t] - k30 x[t],
> > 0 == -k23 n[t] s[t] + k24 t[t],
> > 0 == -k28 e[t] i[t] - k11 h[t] i[t] + k12 k[t] + k29 x[t] + k30
> > x[t]},
> > {n[t], s[t], t[t], h[t], i[t], k[t], e[t], w[t], x[t]}]
> > Solve::"svars": "Equations may not give solutions for all \"solve\"
> \
> > variables."
> > Out[36]=
> > \!\({{t[t] -> \(k23\ n[t]\ s[t]\)\/k24, w[t] -> \(k16\ e[t]\)\/k17,
> > k[t] -> 0, x[t] -> 0, i[t] -> 0}, {t[t] -> \(k23\ n[t]\
> > s[t]\)\/k24,
> > w[t] -> 0, k[t] -> \(k11\ h[t]\ i[t]\)\/k12, x[t] -> 0, e[t]
> ->
> > 0}}\)
> >
> >
> > Why is this happening? is there a way to fool the mathematica to
> solve
> > for the variables?
> >
> > and when you get two solutions for steady state systems, does that
> mean
> > there are two steady states?
> >
> >
> > thanks all in advance for any and all helpful comments.
> >
> > below is the original system prior to steady state reduction
> >
> >
> > Out[38]=
> > \!\(\*
> > RowBox[{"{",
> > RowBox[{
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["a", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(\(-k1\)\ a[t]\ b[t] + k2\ c[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["b", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(\(-k1\)\ a[t]\ b[t] + k2\ c[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["c", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k1\ a[t]\ b[t] - k2\ c[t] - k3\ c[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["d", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k3\ c[t] - k4\ d[t]\ e[t] + k5\ f[t] + k6\ f[t] -
> > k8\ d[t]\ i[t] + 9\ j[t] - k13\ d[t]\ k[t] + k14\
> l[t]\)}],
> > ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["f", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k4\ d[t]\ e[t] - k5\ f[t] - k6\ f[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["j", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k8\ d[t]\ i[t] - 9\ j[t] - k10\ j[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["p", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(\(-k20\)\ o[t]\ p[t] + k21\ q[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["n", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(\(-k18\)\ m[t]\ n[t] + k19\ o[t] - k23\ n[t]\ s[t]
> +
> > k24\ t[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["t", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k23\ n[t]\ s[t] - k24\ t[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["h", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k7\ d[t] - k11\ h[t]\ i[t] + k12\ k[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["k", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k11\ h[t]\ i[t] - k12\ k[t] - k13\ d[t]\ k[t] +
> k14\
> > l[t]\)}],
> > ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["l", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k13\ d[t]\ k[t] - k14\ l[t] - k15\ l[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["u", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(\(-k25\)\ m[t]\ u[t] + k26\ v[t] + k27\ v[t]\)}],
> ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["e", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(\(-k16\)\ e[t] - k4\ d[t]\ e[t] + k5\ f[t] -
> > k28\ e[t]\ i[t] + k17\ w[t] + k29\ x[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["w", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k16\ e[t] + k27\ v[t] - k17\ w[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["g", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k6\ f[t] - k16\ g[t] + k17\ m[t]\)}], ",",
> > RowBox[{
> > RowBox[{
> > SuperscriptBox["m", "\[Prime]",
> > MultilineFunction->None], "[", "t", "]"}],
> > "==", \(k16\ g[t] - k17\ m[t] - k18\ m[t]\ n[t] + k19\ o[t]
> -
> > k25\ m[t]\ u[t] + k26\ v[t]\)}], ",",
> > RowBox[{
>
=== message truncated ===
=====
when riding a dead horse, some dismount.
while others...
write memoirs on the subject of riding a dead horse.
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