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Question: Could you help me to solve Error of Integral?

Question:Could you help me to solve Error of Integral?

permanoon123 165 Maple 2022
integration syntax 2dmath exp user-error sqrt
March 06 2023
0
> 

restart
> 

with(plottools)
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with(plots)
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with(CurveFitting)
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Digits := 100
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"g(t):=10*(e)^((-(t-4000)^(2))/(1300000))+6*(e)^((-(t-6900)^(2))/(1400000))"

proc (t) options operator, arrow, function_assign; 10*exp(-(1/1300000)*(t-4000)^2)+6*exp(-(1/1400000)*(t-6900)^2) end proc

 (1)
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p0 := plot(g(t), t = 0 .. 20000, color = green); plots[display]({p0})

 

````

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v := .7
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disp := 15
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PDE := diff(C(x, t), t) = -v*(diff(C(x, t), x))+disp*(diff(C(x, t), x, x))
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IBC := C(x, 0) = 0, C(0, t) = g(t), (D[1](C))(10000, t) = 0
> 

pds := pdsolve(PDE, [IBC], time = t, range = 0 .. 10000, timestep = 10, numeric, spacestep = 10)

_m2712135358688

 (2)
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k := pds:-plot(x = 6500, t = 0 .. 20000, numpoints = 600); plots[display]({k})

 

NULL

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"f(t):= unapply(Spline( getdata(k)[3][..,1],getdata(k)[3][..,2],'t',degree=2),t): "
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D1 := 15
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E := 20000
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L := 6500
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n := 200
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lambda = `√`(n*Pi/L, (1/2)*D1+`√`((1/4)*D1^2+E(`nπ`/L)^2))
> 

"p(t):=(∫)[0]^(L)f(t) (e(-lambda^2 t) )^dt :"

Error, Got internal error in Typesetting:-Parse : "invalid subscript selector"

"p(t):=(∫)[0]^Lf(t) e(-lambda^2 t) dt :"

  
> 

C(x, t) = sum((2*sin(`nπx`/L)*exp(1)/L*sin(`nπx`/L))*p(t), n = 1 .. 500)

Error, (in sum) summation variable previously assigned, second argument evaluates to 200 = 1 .. 500

  
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uu20000 := [seq(evalf(C(20000-i, 5000)), i = 0 .. 20000, 100)]
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``
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xx := [seq(i, i = 0 .. 20000, 100)]
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p1 := pds:-plot(t = 33000, numpoints = 150, color = red)
> 

plots[display]({p1})

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