Re: NDSolve, FindRoot and shooting method - PROBLEM SOLVED

*To*: mathgroup at smc.vnet.net*Subject*: [mg57503] Re: [mg57430] NDSolve, FindRoot and shooting method - PROBLEM SOLVED*From*: <topolog at gazeta.pl>*Date*: Sun, 29 May 2005 21:00:23 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

For those who are interested: an hour ago I manage to implement shooting method in v. 5.1. Valid code lines look as follows dYdX = EQJ; Y1X1 = {v[z1] == BCV1, v'[z2] == BCV1}; eqset = Join[{dYdX == 0.}, Y1X1]; ndsolut[w_?NumericQ] := NDSolve[eqset /. {W -> w}, v, {z, z1, z2}, SolveDelayed -> True][[1, 1, 2]]; FindRoot[(ndsolut[w])[z2] == BCV3, {w, wdef[[1]], wdef[[2]]}] Regards > > On 5/28/05, topolog at gazeta.pl <topolog at gazeta.pl> wrote: > > Dear Mathematica Users, > > > > This is a valid part of a code that provides shooting method to > > solve equation EQJ = J1(W,z)*v(z) + J2(W,z)*v'(z) + J3(W,z)*v''(z) > > == 0 (--THIS IS THE CORRECT FORM!!--) > > with W - an eigenvalue: > > > > dYdX[W_?NumericQ] := EQJ; (* the equation *) > > Y1X1[W_?NumericQ] := {v[z1] == BCV1, v'[z2] == BCV2}; (* boundary > > conditions, BCV2 is W-dependent *) > > eqset[W_?NumericQ] := Join[{dYdX[W] == 0.}, Y1X1[W]]; (* the set of > > the above *) > > > > (* function that solves eqset for the specified W *) > > ndsolut[W_?NumberQ] := NDSolve[eqset[W], v, {z, z1, z2}][[1, 1, 2]]; > > > > (* searching for W that satisfies another boundary condition *) > > FindRoot[ndsolut[W][z2] == BCV3, {W, W1, W2}] > > > > While in version 4.0 of Mathematica similar code was able to find > > solutions quickly and accurately, the 5.1 version breaks after 100 > > iterations in FindRoot: > > > > FindRoot::cvmit: Failed to converge to the requested accuracy or > > precision within 100 iterations > > > > Any sugestion, please. > > > > Rafal Kosinski > > > > P.S. The J-functions are rather complex so I do not present them > > here. They are dependent of z-coordinate through > > InterpolatingFunction[{{0., 3000.}}, <>][z] and of W in powers from > > 1 to 10.