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Plotting a series of Roots

• To: mathgroup at smc.vnet.net
• Subject: [mg128689] Plotting a series of Roots
• From: William Duhe <wjduhe at loyno.edu>
• Date: Sat, 17 Nov 2012 03:49:35 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net

Bellow is a program that solves a diff eq, then finds a particular valued root for that eq. What I want to do is be able to plot how the root changes as a function of Lambda. 





m = Manipulate[Module[
   {ti, tf, s1},
   imgSize = 375;
   
   ti = 0;(*initial time*)
   tf = 100;(*final plot time*)
   
   
   s1 = NDSolve[{x'[t] == lambda, x[0] == 0}, x, {t, ti, tf}][[1]];
   
   t1 = FindRoot[x[t] == .1 /. s1, {t, tf}];
   
   delta[lambda] := 
    Module[{times, v, s = s1[lambda]}, 
     times = Quiet[
       Chop[FindRoot[x[t] == .1 /. s, {t, #}] & /@ {tf - 1, ti + 1}]];
     v = Flatten[x[t] /. s /. times];
     Subtract @@ v];
   Plot[delta[lambda], {lambda, 0, .007}, Frame -> True, 
     Axes -> False, 
     FrameLabel -> {"lambda", "Change in value of root"}, 
     ImageSize -> imgSize, 
     Epilog -> {Text[ToString[pt, TraditionalForm], pt, {-1.25, 1}], 
       Red, AbsolutePointSize[4], Point[pt]}]
    
    Column[{Plot[Evaluate[{Tooltip[x[t] /. s1, "x[t]"]}], {t, ti, tf},
        PlotRange -> Automatic, AxesLabel -> {"Time", "functions"}, 
       ImageSize -> 350, Exclusions -> Automatic],
      Row[{"x[t] = 1 when ", 
        t1 = 
         Quiet[Chop[
           FindRoot[x[t] == .1 /. s1, {t, #}] & /@ {tf, ti}]]}],
      
      "\n\n"}]], {{lambda, .001}, 0.001, 0.007, 
   Appearance -> "Labeled"}]

• Follow-Ups:
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  • Subscript on plus expression
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