jbendler

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These are questions asked by jbendler

Any suggestions (or perhaps related examples?) illustrating how I might numerically solve for f(t) in the following non-linear integral equation?  In Fortran, I would start with a guess f(t)=T0, and then search in the neighborhood for a minimum (in the error), but I am not familiar with numerical searches and methods in Maple.  Thank you for any suggestions or leads.

(a,b,... etc are all real)


T__0 := 298.

`ΔT` := 25.

0 < beta and beta <= 1

``

f*t = T[0]+`&Delta;T`*[1-exp(-a(int(exp(-b/f(y)), y = y[1] .. t))^beta)]

NULL


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Heaviside2.mw

I am a new user of Maple (Dec 2014).  I am trying to calculate an integral related

to mechanical loss.  Temperature is a variable in the problem (as is time), and if

I use a sinusoidal (sine or cosine) temperature-time relationship, I think all works fine.

A difficulty is that the experiments have two-hour hold times(i.e., 7200 seconds) (followed by 22 hours of sinusoidal temperature variation.)

The experiments run for several weeks or months.

I tried using Heaviside functions to model the hold times.(Constant temperature periods)

Now I am receiving errors such as " Error, (in tools/eval_foo/do) too many levels of recursion..."

Probably the Maple code is crude and/or sloppy. Most of the code is simply the setting of constants in the problem.

I will be grateful for suggestions and comments--the file is attached.  Thank you.  John B

T__2 := 291.4:

T__f := 342.7:

B__f := 1265.:

A__0 := 0.452e-10:

`a__&sigma;` := 1.6072:

`b__&sigma;` := 5.6072:

mu := proc (x) options operator, arrow; .212008+0.21666e-2*x end proc:

t__age := 1800.:

`&sigma;__app` := 3.91:

T__0 := 303.15:

D__0 := proc (x) options operator, arrow; .103172+0.633333e-2*x end proc:

A__ex := B__f*T__f/(T__f-T__2)-`a__&sigma;`*`&sigma;__app`^2:

C__ex := B__f*T__f/(T__f-T__2)-`b__&sigma;`*`&sigma;__app`:

A__00 := A__0*exp(A__ex/T__0):

NULL

NumericEventHandler(invalid_operation = `Heaviside/EventHandler`(value_at_zero = 1)):

tm := proc (t) options operator, arrow; `mod`(t, 86400) end proc:(temperature cycle repeats every 24 hours = 86,400 seconds)

T3 := proc (x) options operator, arrow; (303.15+15.+15*sin((3/2)*Pi+2*Pi*(x-7200)/79200.))*(1-Heaviside(x)+Heaviside(x-7200)) end proc:

F3 := proc (x) options operator, arrow; (Heaviside(x)-Heaviside(x-7200))*303.15 end proc:

ftemp := proc (i) options operator, arrow; evalf(T3(tm(i))+F3(tm(i))) end proc:

C := proc (x) options operator, arrow; A__0*exp(C__ex/ftemp(x)) end proc:

`&tau;__0` := proc (x) options operator, arrow; sqrt(A__00^2*(t__age^mu(ftemp(x)))^2+C(x)^2*x^(2*mu(ftemp(x)))) end proc:

f__0 := proc (z) options operator, arrow; int(1/`&tau;__0`(x), x = 0 .. z) end proc:

g__0 := proc (y) options operator, arrow; D__0(ftemp(y))*exp(f__0(y)^.333333) end proc:

ftim := proc (i) options operator, arrow; 1800.*i end proc:

`&tau;__0`(20);

35860.86195

(1)

f__0(20)

Error, (in tools/eval_foo/do) too many levels of recursion

 

NULL

NULL

NULL

NULL

``

 

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