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Please Help : Error in plotting the solutions of FindRoot

Betatron Steve

Posted 10 years ago

I want to find the roots of an equation using FindRoot as a function of a real parameter K and then plot the real and imaginary solutions vs. the parameter K. The function I'm trying to find the roots is: f[\[CapitalOmega]_,K_]:=1.`\[VeryThinSpace]+(0.00021600988594924262` K^10+(3.81005811091083`^-6-5.617765774643865`^-9 I) K^2 \[CapitalOmega]^8-(1.938898556339015`^-8-4.736384338194926`^-11 I) \[CapitalOmega]^10+K^4 \[CapitalOmega]^6 ((-0.00024705957314623457`+1.7313407860214411`^-7 I)+1.3234889800848443`^-23 \[CapitalOmega]^2)+K^6 \[CapitalOmega]^4 ((0.005208736011404687`\[VeryThinSpace]+8.502422744684232`^-8 I)+4.235164736271502`^-22 \[CapitalOmega]^2)+K^8 \[CapitalOmega]^2 ((0.0021316316776359315`\[VeryThinSpace]+1.0578397620930897`^-8 I)+6.776263578034403`^-21 \[CapitalOmega]^2))/(2.138711742071709`^-6 K^12+0.000021082195553663905` K^10 \[CapitalOmega]^2+0.000051246570978881814` K^8 \[CapitalOmega]^4-3.481280809505708`^-6 K^6 \[CapitalOmega]^6+8.665879028798112`^-8 K^4 \[CapitalOmega]^8-9.45611694948034`^-10 K^2 \[CapitalOmega]^10+3.831913991301718`^-12 \[CapitalOmega]^12) The real solutions Wr : Subscript[W, r][K_,\[Mu]_]:=Re[\[CapitalOmega]/.FindRoot[1.+(0.00021600988594924262 K^10+(3.81005811091083^-6-5.617765774643865^-9 I) K^2 \[CapitalOmega]^8-(1.938898556339015^-8-4.736384338194926^-11 I) \[CapitalOmega]^10+K^4 \[CapitalOmega]^6 ((-0.00024705957314623457+1.7313407860214411^-7 I)+1.3234889800848443^-23 \[CapitalOmega]^2)+K^6 \[CapitalOmega]^4 ((0.005208736011404687+8.502422744684232^-8 I)+4.235164736271502^-22 \[CapitalOmega]^2)+K^8 \[CapitalOmega]^2 ((0.0021316316776359315+1.0578397620930897^-8 I)+6.776263578034403^-21 \[CapitalOmega]^2))/(2.138711742071709^-6 K^12+0.000021082195553663905 K^10 \[CapitalOmega]^2+0.000051246570978881814 K^8 \[CapitalOmega]^4-3.481280809505708^-6 K^6 \[CapitalOmega]^6+8.665879028798112^-8 K^4 \[CapitalOmega]^8-9.45611694948034^-10 K^2 \[CapitalOmega]^10+3.831913991301718^-12 \[CapitalOmega]^12),{\[CapitalOmega],K/Sqrt[\[Mu] (1+K^2)]}]]; And the imaginary solutions Wi : Subscript[W, i][K_,\[Mu]_]:=Im[\[CapitalOmega]/.FindRoot[1.`\[VeryThinSpace]+(0.00021600988594924262` K^10+(3.81005811091083`^-6-5.617765774643865`^-9 I) K^2 \[CapitalOmega]^8-(1.938898556339015`^-8-4.736384338194926`^-11 I) \[CapitalOmega]^10+K^4 \[CapitalOmega]^6 ((-0.00024705957314623457`+1.7313407860214411`^-7 I)+1.3234889800848443`^-23 \[CapitalOmega]^2)+K^6 \[CapitalOmega]^4 ((0.005208736011404687`\[VeryThinSpace]+8.502422744684232`^-8 I)+4.235164736271502`^-22 \[CapitalOmega]^2)+K^8 \[CapitalOmega]^2 ((0.0021316316776359315`\[VeryThinSpace]+1.0578397620930897`^-8 I)+6.776263578034403`^-21 \[CapitalOmega]^2))/(2.138711742071709`^-6 K^12+0.000021082195553663905` K^10 \[CapitalOmega]^2+0.000051246570978881814` K^8 \[CapitalOmega]^4-3.481280809505708`^-6 K^6 \[CapitalOmega]^6+8.665879028798112`^-8 K^4 \[CapitalOmega]^8-9.45611694948034`^-10 K^2 \[CapitalOmega]^10+3.831913991301718`^-12 \[CapitalOmega]^12),{\[CapitalOmega],K/Sqrt[\[Mu](1+K^2)]}]]; When I plotted the real part Wr I got the following numerical roundoff error : Block[{\[Mu] = 100}, Plot[{Subscript[W, r][K, \[Mu]]}, {K, 0, 5}, Frame -> True, PlotRange -> {0, 0.2}, PlotRangePadding -> 0, WorkingPrecision -> 100]] And When I plotted the imaginary part Wi I got also the numerical roundoff error : Block[{\[Mu] = 100}, Plot[{-Subscript[W, i][K, \[Mu]] }, {K, 0, 5}, Frame -> True, PlotRange -> {0, 0.02}, PlotRangePadding -> 0, WorkingPrecision -> 100]] Please, Can you give me now some hint here? I confess that I' m not very savvy with Mathematica and don' t really know which methods are implemented. Attachments:*

I want to find the roots of an equation using FindRoot as a function of a real parameter K and then plot the real and imaginary solutions vs. the parameter K. The function I'm trying to find the roots is:

f[\[CapitalOmega]_,K_]:=1.`\[VeryThinSpace]+(0.00021600988594924262` K^10+(3.81005811091083`*^-6-5.617765774643865`*^-9 I) K^2 \[CapitalOmega]^8-(1.938898556339015`*^-8-4.736384338194926`*^-11 I) \[CapitalOmega]^10+K^4 \[CapitalOmega]^6 ((-0.00024705957314623457`+1.7313407860214411`*^-7 I)+1.3234889800848443`*^-23 \[CapitalOmega]^2)+K^6 \[CapitalOmega]^4 ((0.005208736011404687`\[VeryThinSpace]+8.502422744684232`*^-8 I)+4.235164736271502`*^-22 \[CapitalOmega]^2)+K^8 \[CapitalOmega]^2 ((0.0021316316776359315`\[VeryThinSpace]+1.0578397620930897`*^-8 I)+6.776263578034403`*^-21 \[CapitalOmega]^2))/(2.138711742071709`*^-6 K^12+0.000021082195553663905` K^10 \[CapitalOmega]^2+0.000051246570978881814` K^8 \[CapitalOmega]^4-3.481280809505708`*^-6 K^6 \[CapitalOmega]^6+8.665879028798112`*^-8 K^4 \[CapitalOmega]^8-9.45611694948034`*^-10 K^2 \[CapitalOmega]^10+3.831913991301718`*^-12 \[CapitalOmega]^12)

The real solutions Wr :

Subscript[W, r][K_,\[Mu]_]:=Re[\[CapitalOmega]/.FindRoot[1.+(0.00021600988594924262 K^10+(3.81005811091083*^-6-5.617765774643865*^-9 I) K^2 \[CapitalOmega]^8-(1.938898556339015*^-8-4.736384338194926*^-11 I) \[CapitalOmega]^10+K^4 \[CapitalOmega]^6 ((-0.00024705957314623457+1.7313407860214411*^-7 I)+1.3234889800848443*^-23 \[CapitalOmega]^2)+K^6 \[CapitalOmega]^4 ((0.005208736011404687+8.502422744684232*^-8 I)+4.235164736271502*^-22 \[CapitalOmega]^2)+K^8 \[CapitalOmega]^2 ((0.0021316316776359315+1.0578397620930897*^-8 I)+6.776263578034403*^-21 \[CapitalOmega]^2))/(2.138711742071709*^-6 K^12+0.000021082195553663905 K^10 \[CapitalOmega]^2+0.000051246570978881814 K^8 \[CapitalOmega]^4-3.481280809505708*^-6 K^6 \[CapitalOmega]^6+8.665879028798112*^-8 K^4 \[CapitalOmega]^8-9.45611694948034*^-10 K^2 \[CapitalOmega]^10+3.831913991301718*^-12 \[CapitalOmega]^12),{\[CapitalOmega],K/Sqrt[\[Mu] (1+K^2)]}]];

And the imaginary solutions Wi :

Subscript[W, i][K_,\[Mu]_]:=Im[\[CapitalOmega]/.FindRoot[1.`\[VeryThinSpace]+(0.00021600988594924262` K^10+(3.81005811091083`*^-6-5.617765774643865`*^-9 I) K^2 \[CapitalOmega]^8-(1.938898556339015`*^-8-4.736384338194926`*^-11 I) \[CapitalOmega]^10+K^4 \[CapitalOmega]^6 ((-0.00024705957314623457`+1.7313407860214411`*^-7 I)+1.3234889800848443`*^-23 \[CapitalOmega]^2)+K^6 \[CapitalOmega]^4 ((0.005208736011404687`\[VeryThinSpace]+8.502422744684232`*^-8 I)+4.235164736271502`*^-22 \[CapitalOmega]^2)+K^8 \[CapitalOmega]^2 ((0.0021316316776359315`\[VeryThinSpace]+1.0578397620930897`*^-8 I)+6.776263578034403`*^-21 \[CapitalOmega]^2))/(2.138711742071709`*^-6 K^12+0.000021082195553663905` K^10 \[CapitalOmega]^2+0.000051246570978881814` K^8 \[CapitalOmega]^4-3.481280809505708`*^-6 K^6 \[CapitalOmega]^6+8.665879028798112`*^-8 K^4 \[CapitalOmega]^8-9.45611694948034`*^-10 K^2 \[CapitalOmega]^10+3.831913991301718`*^-12 \[CapitalOmega]^12),{\[CapitalOmega],K/Sqrt[\[Mu](1+K^2)]}]];

When I plotted the real part Wr I got the following numerical roundoff error :

Block[{\[Mu] = 100}, Plot[{Subscript[W, r][K, \[Mu]]}, {K, 0, 5}, Frame -> True, PlotRange -> {0, 0.2}, PlotRangePadding -> 0, WorkingPrecision -> 100]]

enter image description here

And When I plotted the imaginary part Wi I got also the numerical roundoff error :

Block[{\[Mu] = 100}, 
 Plot[{-Subscript[W, i][K, \[Mu]] }, {K, 0, 5}, Frame -> True, 
  PlotRange -> {0, 0.02}, PlotRangePadding -> 0, 
  WorkingPrecision -> 100]]

enter image description here