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Question: Error, (in pdsolve/numeric) unable to handle elliptic PDEs. Help me solve my system please

Question:Error, (in pdsolve/numeric) unable to handle elliptic PDEs. Help me solve my system please

RitaMath 15 Maple 2021
pde numeric pdsolve differential-equations elliptic
January 13 2022
2

system_of_PDE.mw

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NULL
> 

NULL
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Digits := 30; with(PDEtools); with(plots); Ops1 := numpoints = 100; Ops2 := color = magenta; Ops3 := color = blue; Ops4 := color = "BlueViolet"; Ops5 := axes = boxed, shading = zhue, orientation = [40, 50]; a := 0; b := 1; Tf := .5

axes = boxed, shading = zhue, orientation = [40, 50]

  

.5

 (1)
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E := 1480

1480

 (2)
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Ebes := 5990

5990

 (3)
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n0 := 900000

900000

 (4)
> 

ro := 1200

1200

 (5)
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m := 12.6

12.6

 (6)
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f := sig(x, t)-Ebes*`ϵij`(x, t)

sig(x, t)-5990*`ϵij`(x, t)

 (7)
> 

n := 900000*exp(-(sig(x, t)-E*`ϵij`(x, t))/m)

900000*exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t))

 (8)
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NULL
> 

P := 5

5

 (9)
> 

w := 4

4

 (10)
> 

k := 7

7

 (11)
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i := 5

5

 (12)
> 

eq1 := diff(sig(x, t), x, x) = ro*(diff(sig(x, t), x, x))/E+ro*(diff(sig(x, t), t)-Ebes*f/(9000000*exp(-(sig(x, t)-E*`ϵij`(x, t))/m)))*(1+f/m)/(9000000*exp(-(sig(x, t)-E*`ϵij`(x, t))/m))

diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`ϵij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`ϵij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t))

 (13)
> 

 

> 

eq2 := diff(`ϵij`(x, t), t) = f/(9000000*exp(-(sig(x, t)-E*`ϵij`(x, t))/m))

diff(`ϵij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`ϵij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t))

 (14)

NULL

> 

sys := {eq1, eq2}

{diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`ϵij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`ϵij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t)), diff(`ϵij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`ϵij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`ϵij`(x, t))}

 (15)
> 

NULL
> 

IBC1 := {sig(0, t) = P*sin(w*k*i), sig(10, t) = P*sin(w*k*i), sig(x, 0) = 0, sig(x, 1) = 0, `ϵij`(x, 0) = 0}

{sig(0, t) = 5*sin(140), sig(10, t) = 5*sin(140), sig(x, 0) = 0, sig(x, 1) = 0, `ϵij`(x, 0) = 0}

 (16)
> 

S := 1/100; Ops := spacestep = S, timestep = S; Sol1 := pdsolve(sys, IBC1, [sig, `ϵij`], numeric, time = t, range = a .. b, Ops)

1/100

  

spacestep = 1/100, timestep = 1/100

  

Error, (in pdsolve/numeric) unable to handle elliptic PDEs

  
> 

``

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