Re: Solve transcendental functions
- To: mathgroup at smc.vnet.net
- Subject: [mg21138] Re: Solve transcendental functions
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Fri, 17 Dec 1999 01:21:38 -0500 (EST)
- Organization: Wolfram Research, Inc.
- References: <831v41$g3d@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
sandmann at mip.sdu.dk wrote: > > If i got the function > f[x]:=x^2-2Cos[a*x]/a > and tries to Solve[f[x]==f'[x],x] > I get > The equations appear to involve transcendental functions of the > variables in an essentially non-algebraic way. > > How do I solve this problem ? > Regards Niels Sandmann > > Sent via Deja.com http://www.deja.com/ > Before you buy. You can find solutions for particular values of a, provided you supply a starting point for a Newton-type iteration. f[x_,a_] := x^2-2Cos[a*x]/a parametrizedSolve[f_, a_?NumberQ, init_] := FindRoot[Evaluate[f[x,a]==D[f[x,a],x]], {x,init}, AccuracyGoal->15, WorkingPrecision->20] For example, if I want to handle the case where a is 1, starting near x=2, I can do as below. In[110]:= parametrizedSolve[f, 1, 2] Out[110]= {x -> 2.1999981850434100730} Starting at x=0 gives In[111]:= parametrizedSolve[f, 1, 0] Out[111]= {x -> -0.41895202574023425297} Daniel Lichtblau Wolfram Research