Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

Topic: Subscript on plus expression
Replies: 16   Last Post: Dec 3, 2012 3:18 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Bob Hanlon

Posts: 906
Registered: 10/29/11
Re: Plotting a series of Roots
Posted: Nov 19, 2012 5:05 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Not clear what you are trying to accomplish. The following example
provides some approaches

s1[lambda_, t_] =
x[t] /. DSolve[{x'[t] == lambda, x[0] == 0}, x[t], t][[1]]

lambda t


t1[lambda_, value_] = t /. Solve[s1[lambda, t] == value, t][[1]]

value/lambda


s1[lambda, t1[lambda, value]]

value


Manipulate[
Module[
{ti = 0,
tf = 100,
pt = {t1[lambda, value], value}},
Plot[s1[lambda, t], {t, ti, tf},
PlotRange -> {0, 0.7},
Epilog -> {
Text[
{NumberForm[pt[[1]], {4, 1}],
NumberForm[pt[[2]], {4, 2}]},
pt, {1.5, -1.5}],
LightGray,
Line[{{ti, value}, pt}],
Line[{
{t1[lambda, value], 0}, pt}],
Red,
AbsolutePointSize[5],
Point[pt]}]],
{{value, 0.1}, 0, 0.7, 0.01,
Appearance -> "Labeled"},
{{lambda, 0.001}, 0.001, 0.007, 0.00025,
Appearance -> "Labeled"}]


Bob Hanlon


On Sat, Nov 17, 2012 at 3:49 AM, William Duhe <wjduhe@loyno.edu> wrote:
> 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"}]
>





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.