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

*To*: mathgroup at smc.vnet.net*Subject*: [mg29098] Re: [mg29085] Re: Why can't Nsolve find a solution to this ?*From*: BobHanlon at aol.com*Date*: Tue, 29 May 2001 02:57:24 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

?NSolve "NSolve[lhs==rhs, var] gives a list \ of numerical approximations to the \ roots of a polynomial equation. \ NSolve[{eqn1, eqn2, ... }, {var1, \ var2, ... }] solves a system of \ polynomial equations."* Button[More\[Ellipsis], ButtonData :> "NSolve", Active -> True, ButtonStyle -> "RefGuideLink"] Your equations are not polynomials in the unknown variables. Use FindRoot. FindRoot[{1.7863852^2== v^2 + u^2, u *Tan[u] == v},{u, 1.},{v, 1.}] {u -> 0.9860552092989878, v -> 1.4895862536291804} Bob Hanlon In a message dated 2001/5/27 6:22:44 PM, REMOOVE_THIS_drkirkby at AND_THIS_ntlworld.com writes: >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. >