Re: field line with NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg58045] Re: field line with NDSolve*From*: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>*Date*: Fri, 17 Jun 2005 05:18:42 -0400 (EDT)*Organization*: Uni Leipzig*References*: <d8rl77$jnl$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, you will never get a result as long ais you use variables with underscores in it, an underscore is a short form for Pattern[] and and "eqn_bnd" is Pattern[eqn,bnd] and not a symbol. Regards Jens <topolog at gazeta.pl> schrieb im Newsbeitrag news:d8rl77$jnl$1 at smc.vnet.net... > Hi everybody! > > I am trying to obtain a magnetic field line in > 3d, i.e. z(x{y),y). > So I have magnetic induction vector B = (Bx, By, > Bz), where > Bi=Bi(x,y,z), i={x,y,z}. By the definition I set > an unit vector in > direction y: b = B / Abs[By] = (bx, by, bz) and > replace coordinates > x and z with functions x[y], z[y]. The final > step is to integrate > the set of 2 equations: > x'[y] = bx > z'[y] = bz > > In version 4.0 of Mathematica I was able to > solve that with the code > below, but in 5.1 I am not anymore. I suppose > the conflict exists in > passing arguments as symbolic, since B depends > on z through > InterpolatingFunction(s) and after replacing > z -> z[y], I got > InterpolatingFunction[{{0., 1000.}}, <>][z[y]]. > But I am not sure > how to manage this ... > > B = {Bx, By, Bz}; > b = B/Abs[By] /. {x -> x[y], z -> z[y]}; > r = {x[y], z[y]}; > eqn_b = {D[r[[1]], y] == b[[1]], D[r[[2]], y] == > b[[3]]} > > bnd_con = {x[ymin] == xmax/2, z[ymin] == > zmax/10}; > eqn_bnd = Join[eqn_b, bnd_con]; > B_line = NDSolve[eqn_bnd, r, {y, ymin, ymax}]; > > The error I get is: > > NDSSolve::nlnum : The function value {...a large > expression...} is > not a list of numbers with dimmensions {2} at > y={...a value...} > > Any hints, please. > > Ragards > Rafal Kosinski > > > > -- > Promocja! Format 15x20 tylko 99gr! > Zamów odbitki cyfrowe online - odbierz za darmo > w EMPiK-u lub wy¶lemy Ci je poczt± > http://gazeta.empikfoto.pl >