Re: calculations in findRoot
- To: mathgroup at smc.vnet.net
- Subject: [mg100162] Re: calculations in findRoot
- From: dh <dh at metrohm.com>
- Date: Wed, 27 May 2009 04:04:37 -0400 (EDT)
- References: <gv7qv0$ar1$1@smc.vnet.net>
Hi, unfortunately, your message is garbeled. But have a look at: http://forums.wolfram.com/mathgroup/archive/2009/May/msg00295.html Daniel hesami.phy at gmail.com wrote: > Hello, > In my program(with mathematica 5), I want to determine rB=R(peak),rV=R > (valley); > r1[l],r2[l] if vV[l]=EF=82=A3EE=EF=82=A3vB[l]. > question: > in option FindRoot[D[vt[l,r],r]==0,{r,r0}] How I choose r0 until for > each "l" solution rB=R(peak),rV=R(valley),r1[l],r2[l] be correct? > Pleas guide me. > Thanks. > > my program: > > vt[l_, r_] := v0/\((1 + Exp[\(( > r - R0)\)/a0])\) + 1.439*\ z1\ z2\ /r\ + \ \((\((197.327)\)^2\ \ l > \ \(( > l + 1)\))\)/\((2\ m\ r\^2)\)\) > > R0=8.9436;a0=0.626;v0=-81.9;z1=8;z2=62;EE=50;l=61;m=13496.77059;hc=197.327; > > > rB[l_]:=FindRoot[D[vt[l,r],r]==0,{r,10}] > > vB[l_]:=vt[l,r]/.{r\[Rule]rB[l][[1,2]]} > > rV[l_]:=FindRoot[D[vt[l,r],r]==0,{r,8}] > > vV[l_]:=vt[l,r]/.{r\[Rule]rV[l][[1,2]]} > > r1[l_]:=If[vV[l] > =E2=89=A4EE=E2=89=A4vB[l],FindRoot[vt[l,r]-EE==0,{r,rV[l][[1,2]],rB[l][[1,2]]}]] > > r2[l_]:=If[vV[l]=E2=89=A4EE=E2=89=A4vB[l],FindRoot[vt[l,r]-EE==0,{r,rB[l][[1,2]],14}]] > > h=CE=A9[l_]:=Sqrt[Abs[((hc)^2/m)*D[vt[l,r],{r,2}]]]%/.r\[Rule]rB[l][[1,2]]; > > \!\(s[l_] := If[vV[ > l] =E2=89=A4 EE =E2=89=A4 vB[ > l], Sqrt[2*m/\((hc)\)^2]*\ > NIntegrate[\@\((\(-EE\) + vt[l, r])\), {r, \(r1[l]\)[\ > ([1, > 2]\)], \(r2[l]\)[\([1, 2]\)]}]] // Chop\) > > t[l_]:=Which[vB[l]=E2=89=A4EE,1/(1+Exp[(2 =CF=80 (vB[l]- > EE)/h=CE=A9[l])]),vV[l]=E2=89=A4EE=E2=89=A4vB[l],1/(1+Exp[2 s[l]]),EE=E2=89=A4vV[l],0]//Chop > > =CF=83[l_,EE_]:==CF=80*(hc)^2*(2 l+1)*t[l]/(2*m*EE) > > =CF=83[EE_]:=10 (=CF=83[0, > EE]+=CF=83[1,EE]+=CF=83[2,EE]+=CF=83[3,EE]+=CF=83[4,EE]+=CF=83[5,EE]+=CF=83[6,EE]+=CF=83[7,EE]+=CF=83[8,EE]+=CF=83 > [9, > EE]+=CF=83[10,EE]+=CF=83[11,EE]+=CF=83[12,EE]+=CF=83[13,EE]+=CF=83[14,EE]+=CF=83[15,EE]+=CF=83 > [16, > EE]+=CF=83[17,EE]+=CF=83[18,EE]+=CF=83[19,EE]+=CF=83[20,EE]+=CF=83[21,EE]+=CF=83[22,EE]+=CF=83 > [23,EE]+=CF=83[ > 24,EE]+=CF=83[25,EE]+=CF=83[26,EE]+=CF=83[27,EE]+=CF=83[28,EE]+=CF=83[29,EE]+=CF=83[ > 30,EE]+=CF=83[31,EE]+=CF=83[32,EE]+=CF=83[33,EE]+=CF=83[34,EE]+=CF=83[35,EE]+=CF=83[ > 36,EE]+=CF=83[37,EE]+=CF=83[38,EE]+=CF=83[39,EE]+=CF=83[40,EE]+=CF=83[41,EE]+=CF=83[ > 42,EE]+=CF=83[43,EE]+=CF=83[44,EE]+=CF=83[45,EE]+=CF=83[46,EE]+=CF=83[47,EE]+=CF=83[ > 48,EE]+=CF=83[49,EE]+=CF=83[50,EE]+=CF=83[51,EE]+=CF=83[52,EE]+=CF=83[53,EE]+=CF=83[ > 54,EE]+=CF=83[55,EE]+=CF=83[56,EE]+=CF=83[57,EE]+=CF=83[58,EE]+=CF=83[59,EE]) > > {EE,=CF=83[EE]} > > ({50, 6.025565489081184`*10^-8}\) > > > but soultion below is corect.", > > > {50, 6.521257897`*10^-8} >