Re: loglogplot

*To*: mathgroup at smc.vnet.net*Subject*: [mg73097] Re: loglogplot*From*: dh <dh at metrohm.ch>*Date*: Fri, 2 Feb 2007 05:15:23 -0500 (EST)*References*: <eps7ek$908$1@smc.vnet.net>

Hi Lynn, there are several things wrong. First, if you solve our diff equation for y'': Out[128]//OutputForm= 2 x y[x] - 2 y[x] y'[x] + x y'[x] {{y''[x] -> --------------------------------}} x y[x] you see that you will have troubles near x=0. Therefore, integrate the DG not from 0 but from 0.00001. Second, Evaluate will only work if its on the top level of an argument. E.g. a = 1; f[x_] := Print[Hold[x]]; SetAttributes[f, HoldAll]; f[2 Evaluate[a]] will print: Hold[2 Evaluate[a]] not 2 *1 as you may have expected. Therefore it is much better to do the substitution of the interpolating function as early as possible, e.g: sol=y /. NDSolve[{2 y'[x] y[x] + x y''[x] y[x] - x (y'[x])^2 == x y[x], y[0.00001] == 1, y'[0.00001] == 0}, y, {x, 0.00001, 1}, MaxSteps -> 1000][[1]] Further use NItegrate instead of Integrate f[w_?NumberQ] := 2 NIntegrate[(sol[x])^-1 x/Sqrt[x^2 - w^2], {x, w, 1}] finally: LogLogPlot[{f[w], w}, {w, 0.01, 0.99}] Daniel lynn wrote: > Hello, > > I have some problems during the processes. > > \!\(sol = > NDSolve[{2\[Times]\(y'\)[x]\[Times]y[x] + > x\[Times]\(y''\)[x]\[Times]y[x] - > x\[Times]\((\(y'\)[x])\)\^2 \[Equal] x\[Times]y[x], > y[0.00001] \[Equal] 1, \(y'\)[0.00001] \[Equal] 0}, y, {x, 0, > 1}, > MaxSteps \[Rule] 1000]\[IndentingNewLine] > f[w_?NumberQ] := > 2\[Times]Integrate[\((Evaluate[y[x] /. sol])\)\^\(-1\)\[Times] > x\/\@\(x\^2 - w\^2\), {x, w, 1}]\[IndentingNewLine] > << Graphics`Graphics`\[IndentingNewLine] > curve = LogLogPlot[{f[w], w}, {w, 0.01, 0.99}]\) > > However, the prcesses work well when I just "Plot" the curve, not > "LogLogPlot" it. > I don't know what's wrong.... > > Thanks a lot!!! >