Re: multiple subscripted variables in NDSolve; dsfun

*To*: mathgroup at smc.vnet.net*Subject*: [mg22009] Re: [mg21979] multiple subscripted variables in NDSolve; dsfun*From*: "stephen e. schwartz" <ses at bnl.gov>*Date*: Thu, 10 Feb 2000 02:25:52 -0500 (EST)*References*: <200002071802.NAA08387@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hello Hartmut, you correctly identified the problem. Thank you! I flattened the tables in my lists of initial conditiions, equations, and arguments of NDSolve and voila. My faith is restored. -steve At 10:00 AM +0100 2/8/00, Hartmut Wolf wrote: >stephen e. schwartz schrieb: >> > >> I am attempting to use NDSolve (Mathematica 4.0.1.0, mac) to solve a set >>of coupled >> ODEs in the time variable t. Initially I had a set of variables a[i][t], >> which solve just fine. The index [i] ranges {1, nc} >> >> Then I wanted to add another set of variables mn[i][t]. Attempts to solve >> the set (it is still a set of ODEs) brings the response: >> >> NDSolve::dsfun: "{a[1][t], mn[1][t]} cannot be used as a function" >> >> I had defined the argument of NDSolve as a table, >> >> NDSolve[{eq, ic}, Table[{a[i][t], mn[i][t]}, {i, nc}] where eq, ic are >> tables of equations and initial conditions, resp. >> >> If I "fool" Mathematica by renaming the variable mn[i] as a[i + nc] and >>suitably >> modify my equations and initial conditions, and the range if the index, the >> set solves just fine, although I am very unhappy about the notation in that >> a and mn represent very different variables. >> >> So, am I correct in inferring that the compact notation for a set of >> coupled indexed equations (Mathematica book, 4th ed, sec 3.9.7, page >>926) works >> only for a single variable name? >> >> Is there a more elegant fix? >> > >Dear Stephen, > >if you rework the example in §3.5.10 of The Mathematica Book > >In[1]:= DSolve[{y[x] == -z'[x], z[x] == -y'[x]}, {y, z}, x] > >to your manner of denoting the variables > >In[2]:= >DSolve[{a[1][t] == -mn[1]'[t], mn[1][t] == -a[1]'[t]}, {a[1], mn[1]}, t] > >you'll see it isn't that. Instead you introduced Table > >In[3]:= >DSolve[{a[1][t] == -mn[1]'[t], mn[1][t] == -a[1]'[t]}, > Table[{a[i], mn[i]}, {i, 1}], t] > >and it stops working -- because now you no longer have a flat list of >variables. >So > >In[4]:= >DSolve[{a[1][t] == -mn[1]'[t], mn[1][t] == -a[1]'[t]}, > Flatten[Table[{a[i], mn[i]}, {i, 1}]], t] > > >Kind regards, Hartmut - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - PLEASE NOTE NEW AREA CODE: 516 --> 631 Stephen E. Schwartz, Senior Scientist mailto:ses at bnl.gov Environmental Chemistry Division Phone: (631) 344-3100 Brookhaven National Laboratory Fax: (631) 344-2887 Bldg. 815E (75 Rutherford Dr.) PO Box 5000 Sec'y: (631) 344-3275 Upton NY 11973-5000 ftp://ftp.ecd.bnl.gov//pub/steve Home Page: http://www.ecd.bnl.gov/steve/schwartz.html Secretary: Maggie Marsch (mailto:mmarsch at bnl.gov) Tropospheric Aerosol Program (TAP) Home Page: http://www.tap.bnl.gov - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

**References**:**multiple subscripted variables in NDSolve; dsfun***From:*"stephen e. schwartz" <ses@bnl.gov>