Re: Help with findroot

*To*: mathgroup at smc.vnet.net*Subject*: [mg9172] Re: Help with findroot*From*: weber at math.uni-bonn.de (Matthias Weber)*Date*: Tue, 21 Oct 1997 02:02:46 -0400*Organization*: RHRZ - University of Bonn (Germany)*Sender*: owner-wri-mathgroup at wolfram.com

In article <624ijs$m2j at smc.vnet.net>, darrmis at aol.com (Darrmis) wrote: > I'm having a problem using findroot to solve an equation. Perhaps > someone > could shed some light on what's wrong. > > FindRoot[Sqrt[x/(1.2 10^ -4)]==-0.1*Tan[Sqrt[x/(1.2*10^ > -4)]],{x,0.1,0.1,2}] > > Mathematica 3. returns a value of -0.07 for x which is not anywhere > close to correct. > Further, I've tried several different starting values and min/max > limits, but > a negative answer is always returned. Eventually I'de like to compile > a list > of all the roots of the equation up to, say, x=1000, but I can't even > get one > right now. > > Thanks, > > Karl Kevala For a general (say continous function) it is harder to find a zero than you might think. Because of this, you cannot expect a program or a human or whatever to find all or just one zero of any function you cook up. In your case, combined insight in the problem and in Mathematica´s abilities to solve equations numerically are quite helpfull. (It might also be helpfull to plot the equation to see where the zeroes of your function are hidden.) First, replacing x/(1.2 10^ -4) by y reduces the problem slightly and non-essentially to finding zeroes of y==0.1*Tan[y], say up to y=10^6. This is still too hard to be put before Mathematica, but from elementary calculus you know that this function has simple poles at Pi/2 + k Pi so that FindRoot[y==0.1*Tan[y], {y,Pi/2-0.001}] would be my try to get Mathematica to solve this problem, using Newton´s method which is very appropriate for that problem. Using this it shouldn´t be hard to find all zeroes of your function in any range. Proving that you did in fact find all requires then some more mathmatical skills which you also can learn in any good undergraduate math text but not in the Mathematica handbook. If you are really interested in locating zeroes of (say) meromorphic functions (like yours), you should can consult text books on complex variables where more sophisticated techniques are available. Matthias Weber

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