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

*To*: mathgroup at smc.vnet.net*Subject*: [mg29099] AW: [mg29085] Re: Why can't Nsolve find a solution to this ?*From*: Matthias.Bode at oppenheim.de*Date*: Tue, 29 May 2001 02:57:25 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hello David, I am unable to tell you why NSolve does not find the desired solution but In[3]:= FindRoot[ {1.7863852^2 == v^2 + u^2, u Tan[u] == v}, {u, 1}, {v, 1}] Out[3]= {u -> 0.986055, v -> 1.48959} does the trick - numerically. Best regards, Matthias Bode Sal. Oppenheim jr. & Cie. KGaA Koenigsberger Strasse 29 D-60487 Frankfurt am Main GERMANY Tel.: +49(0)69 71 34 53 80 Mobile: +49(0)172 6 74 95 77 Fax: +49(0)69 71 34 6380 E-mail: matthias.bode at oppenheim.de Internet: http://www.oppenheim.de 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