Re: Why can't Nsolve find a solution to this ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg29101] Re: Why can't Nsolve find a solution to this ?*From*: bghiggins at ucdavis.edu (Brian Higgins)*Date*: Tue, 29 May 2001 02:57:26 -0400 (EDT)*References*: <9eruh1$3l7@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

David, Try FindRoot when equations involve trancendental functions. For example: In[1]:=sol = u*Tan[u] - v /. Solve[W^2 == u^2 + v^2, v] Out[1]={Sqrt[-u^2 + W^2] + u*Tan[u], -Sqrt[-u^2 + W^2] + u*Tan[u]} In[2]:=FindRoot[Last[sol /. W -> 1.7869] == 0, {u, 1}] Out[2]={u -> 0.986169} Cheers, Brian David Kirkby <REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com> wrote in message news:<9eruh1$3l7 at smc.vnet.net>... > I'd like if possible to obtain an analytical solution to the > following two simultaneous equations, but given that is apparently not > likely to be found, I thought of a using NSolve to get a numerical one. > However, Nsolve can't seem to find a solution, despite the fact that if > I write a computer programme in 5 minutes or less to solve it > numerically. Am I missing something here ?? > > The equations arrise from optical waveguides: > W^2=u^2 + v^2 > v=u tan(u) > > W is known in advance, so I want to find the 2 variables u and v using > the above 2 equations. I've tried: > > In[2]:= NSolve[ {1.7863852^2== v^2 + u^2, u Tan[u] == v},{u,v}] > > Solve::tdep: The equations appear to involve the variables to be solved > for in > an essentially non-algebraic way. > > 2 2 > Out[2]= NSolve[{3.19117 == u + v , u Tan[u] == v}, {u, v}] > > Yet I know there is a solution to this : u->0.986, v->1.4893. > > Any suggestions on how to get Mathematica to find such solutions ??? > > I'm using Mathematica 4.01 on a Sun SPARCstation 20, with Solaris 8.