Re: Solvability sensitive to small changes in numerical input

*To*: mathgroup at smc.vnet.net*Subject*: [mg47516] Re: [mg47494] Solvability sensitive to small changes in numerical input*From*: Oleksandr Pavlyk <pavlyk at phys.psu.edu>*Date*: Thu, 15 Apr 2004 03:39:22 -0400 (EDT)*Organization*: Penn State University; Department of Physics*References*: <200404141116.HAA27286@smc.vnet.net>*Reply-to*: pavlyk at phys.psu.edu*Sender*: owner-wri-mathgroup at wolfram.com

Hi Gareth, I think you should use FindRoot instead of Solve. It is also better suited for numerics. I took the liberty to transform your equation slightly Clear[f]; f[a1_, a2_, b_, prec_:30] := Module[ {c, t1, t2, t3, n0}, c = 2*(b/(b - 1)); t1 = 1/a1^c; t2 = 1/a2^c; n0 = (b*(t1+t2))^(1/c); SetPrecision[ n /. Assuming[n \[Element] Reals, FindRoot[ 0 == b*t1*(t2 + n^c) + b*t2*(t1 + n^c) - 2*(t1 + n^c)*(t2 + n^c) , {n, n0}]], prec] ]; f[2., 0.05, 6.21] 27.3331323380492889896231645253 I have chosen the initial point for the FindRoot, by assuming, in the first approximation that t1 and t2 are small compared to n^c. Best regards, Sasha Gareth J. Russell wrote: > Hi, > > I have a function that includes the Solve command > > f[a1_, a2_, b_] := Module[{c}, > > c = 2*b/(b - 1); > > Solve[b/(1 + (a1*n)^c) + b/(1 + (a2*n)^c) == 2, n] > > ] ] > > but it seems very sensitive to the numerical input. For example, > > f[2., 0.05, 6.19] > > and > > f[2., 0.05, 6.21] > > Produce the error "The equations appear to involve the variables to be > solved for in an essentially non-algebraic way." > > Whereas > > f[2., 0.05, 6.20] > > produces the solutions > > {{n -> -23.8725 - 13.2503i]}, {n -> -23.8725 + 13.2503i}, { > n -> 0.183281 - 0.707873i}, {n -> 0.183281 + 0.707873i]}, {n -> 27. > 3032}} > > Can anyone enlighten me as to what is going on here? Other peoples' work > suggests that, given a1 = 2., it should be possible to get numerical > solutions for a large range of values of a2 and b. > > If it makes a differences we make the assumptions a1 > 0, a2 > 0, a2 < > a1 and b >= 1. > > Oh, and v5.0.1.0 on Mac OS X > > Thanks! > > Gareth Russell > > Columbia University

**References**:**Solvability sensitive to small changes in numerical input***From:*"Gareth J. Russell" <gjr2008@columbia.edu>