Re: Help with findroot

*To*: mathgroup at smc.vnet.net*Subject*: [mg9173] Re: [mg9169] Help with findroot*From*: David Withoff <withoff>*Date*: Tue, 21 Oct 1997 02:02:47 -0400*Sender*: owner-wri-mathgroup at wolfram.com

> 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 One of the more useful ways to understand this type of example is to look at plots of the functions, such as Plot[{Sqrt[x/(1.2 10^-4)], -0.1 Tan[Sqrt[x/(1.2 10^-4)]]}, {x, 0, .01}, PlotRange -> {-5, 15}] which correctly suggests that this equation has an infinite number of solutions (as well as some awkward singularities that are likely to make the problem computationally challenging). There is a solution near .0003 In[12]:= FindRoot[Sqrt[x/(1.2 10^ -4)]==-0.1*Tan[Sqrt[x/(1.2*10^-4)]], {x,.0003}] Out[12]= {x -> 0.000319609} and another one near .0027 In[22]:= FindRoot[Sqrt[x/(1.2 10^ -4)]==-0.1*Tan[Sqrt[x/(1.2*10^-4)]], {x,.0027}] Out[22]= {x -> 0.00268874} and so forth. Because of the singularities, you may need to choose starting values that are rather close to the solution in order for the algorithm to converge to the solution that you want. The plots can be very useful in choosing good starting values. Dave Withoff Wolfram Research