Re: field line with NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg58055] Re: field line with NDSolve*From*: dh <dh at metrohm.ch>*Date*: Fri, 17 Jun 2005 05:19:06 -0400 (EDT)*References*: <d8rl77$jnl$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi Rafal, here is a working example of your problem: xmax = 1; ymin = 0; ymax = 1; zmax = 1; Bx = Sin[y]; By = Cos[x]; Bz = z; B = {Bx, By, Bz}; b = B/Abs[By] /. {x -> x[y], z -> z[y]}; r = {x[y], z[y]}; eqnb = {D[r[[1]], y] == b[[1]], D[r[[2]], y] == b[[3]]} bndcon = {x[ymin] == xmax/2, z[ymin] == zmax/10} eqnbnd = Join[eqnb, bndcon] Bline = NDSolve[eqnbnd, r, {y, ymin, ymax}] ParametricPlot3D[Evaluate[{x[y], y, z[y]} /. Bline], {y, ymin, ymax}] sincerely, Daniel topolog at gazeta.pl wrote: > 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 > > >