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

*To*: mathgroup at smc.vnet.net*Subject*: [mg29121] Re: [mg29085] Re: Why can't Nsolve find a solution to this ?*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Wed, 30 May 2001 05:50:36 -0400 (EDT)*References*: <200105272204.SAA03679@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

David Kirkby wrote: > > 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. > > -- > Dr. David Kirkby Ph.D, > email: REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com > former email address: davek at DELLETE_THIS_medphys.ucl.ac.uk > web page: http://www.david-kirkby.co.uk > Amateur radio callsign: G8WRB NSolve handles polynomial systems with finitely many solutions. For transcendental systems you can use FindRoot. Below I do this using random guess values each between 0 and 1. In[26]:= FindRoot[{1.7863852^2== v^2 + u^2, u Tan[u] == v}, {u,Random[]}, {v,Random[]}] Out[26]//InputForm= {u -> 0.9860552189827669, v -> 1.4895862496875691} Daniel Lichtblau Wolfram Research

**References**:**Re: Why can't Nsolve find a solution to this ?***From:*David Kirkby <REMOOVE_THIS_drkirkby@AND_THIS_ntlworld.com>