Re: Higher precision in Error function Erf[] needed.

*To*: mathgroup at smc.vnet.net*Subject*: [mg127093] Re: Higher precision in Error function Erf[] needed.*From*: Cyril <cyril.stephanos at gmail.com>*Date*: Fri, 29 Jun 2012 04:52:59 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jsbt4i$6pq$1@smc.vnet.net> <jseeua$i3d$1@smc.vnet.net>

On Wednesday, June 27, 2012 10:06:34 AM UTC+2, Ray Koopman wrote: > On Jun 26, 1:50 am, Cyril <cyril.stepha... at gmail.com> wrote: > > Hi everyone > > > > I am using the error function as part of differential equations I am solving with NDSolve. > > Unfortunately, for certain parameters, the error function Erf[] starts oscillating and yielding wrong values. > > > > The oscillation does not show when I plot the error function itself, but when I plot this expression > > > > Plot[Exp[8*(10 - Abs[10 - 20000*x])]*(1 - Erf[(8*(10 - Abs[10 - 20000*x]))^(1/2)]), {x, 0, 1*10^(-3)}, PlotRange -> Full] > > > > it becomes visible. > > > > When I do the integration for error function with NDSolve manually and plot the expression, the oscillation vanishes for high values of PrecisionGoal and WorkingPrecision, e.g. > > > > Plot[ Exp[8*(10 - Abs[10 - 20000*x])]*(1 - NIntegrate[ 2/Sqrt[Pi] Exp[-t^2], {t, 0, (8*(10 - Abs[10 - 20000*x]))^(1/2)}, PrecisionGoal -> 40, WorkingPrecision -> 40]), {x, 0, 1*10^(-3)}, PlotRange -> Full] > > > > The oscillation of Erf[] is not only visible in the plot, it also leads to wrong results in my calculations. > > > > I tried to increase the precision of Erf[] by using N[Erf[],n] with very high values for n - as described in the Mathematica help - but it does not change anything. > > > > Solving the Integral for the error function manually with NDSolve yields two problems. It is very slow - it takes about three minutes on my computer (I have to solve many equations) - whereas Erf[] is much faster. And it seems that I cannot use NDSolve as part of an equation I want to solve with NDSolve itself. > > > > Is there a possibility to increase the precision of Erf[] and obtain more accurate results? > > > > Thank you in advance for your help. > > > > Best regards > > Cyril > > Change (1 - Erf[...]) to Erfc[...] . Ok, that was easy and works perfect. Thanks a lot! Although it was not what I expected. Is there a possibility to alter the precision of Erf[]? Best regards Cyril