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Errors in solving coupled pdes

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Errors in solving coupled pdes

1

$begingroup$

I am trying to solve following coupled PDEs:

I am not sure about suitable BCs.

 ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x, 

t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],

D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara - 

gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

V[x, t] == 0 /. x -> 0,

V[x, t] == 0 /. x -> 1,

Rho[x, t] == 0 /. x -> 0,

Rho[x, t] == 0 /. x -> 1,

T[x, t]   == 0 /. x -> 0,

T[x, t]   == 0 /. x -> 1,

D[T[x, t], x] == 0 /. x -> 1,

V[x, 0] == Sin[Pi*x/L],

Rho[x, 0] == 0,

T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}] 

General::ivar: 3 is not a valid variable.
........
Also, how i can import variable gpara in .txt format to this code?

differential-equations

share|improve this question

edited 2 hours ago

Danial

asked 2 hours ago

Danial Danial

62

New contributor

Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

1

$begingroup$

I am trying to solve following coupled PDEs:

I am not sure about suitable BCs.

 ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x, 

t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],

D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara - 

gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

V[x, t] == 0 /. x -> 0,

V[x, t] == 0 /. x -> 1,

Rho[x, t] == 0 /. x -> 0,

Rho[x, t] == 0 /. x -> 1,

T[x, t]   == 0 /. x -> 0,

T[x, t]   == 0 /. x -> 1,

D[T[x, t], x] == 0 /. x -> 1,

V[x, 0] == Sin[Pi*x/L],

Rho[x, 0] == 0,

T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}] 

General::ivar: 3 is not a valid variable.
........
Also, how i can import variable gpara in .txt format to this code?

differential-equations

share|improve this question

edited 2 hours ago

Danial

asked 2 hours ago

Danial Danial

62

New contributor

Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

I am trying to solve following coupled PDEs:

I am not sure about suitable BCs.

 ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x, 

t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],

D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara - 

gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

V[x, t] == 0 /. x -> 0,

V[x, t] == 0 /. x -> 1,

Rho[x, t] == 0 /. x -> 0,

Rho[x, t] == 0 /. x -> 1,

T[x, t]   == 0 /. x -> 0,

T[x, t]   == 0 /. x -> 1,

D[T[x, t], x] == 0 /. x -> 1,

V[x, 0] == Sin[Pi*x/L],

Rho[x, 0] == 0,

T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}] 

General::ivar: 3 is not a valid variable.
........
Also, how i can import variable gpara in .txt format to this code?

differential-equations

share|improve this question

edited 2 hours ago

Danial

asked 2 hours ago

Danial Danial

62

New contributor

Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

 ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x, 

t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x],

D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara - 

gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

V[x, t] == 0 /. x -> 0,

V[x, t] == 0 /. x -> 1,

Rho[x, t] == 0 /. x -> 0,

Rho[x, t] == 0 /. x -> 1,

T[x, t]   == 0 /. x -> 0,

T[x, t]   == 0 /. x -> 1,

D[T[x, t], x] == 0 /. x -> 1,

V[x, 0] == Sin[Pi*x/L],

Rho[x, 0] == 0,

T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}] 

share|improve this question

edited 2 hours ago

Danial

asked 2 hours ago

Danial Danial

62

New contributor

Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

edited 2 hours ago

Danial

asked 2 hours ago

Danial Danial

62

New contributor

Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Danial Danial

62

New contributor

Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 2 hours ago

Danial Danial

62

1 Answer
1

active

oldest

votes

4

$begingroup$

Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:

ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {

   D[V[x, t], 

     t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) + 

     Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

   D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x], 

   D[T[x, t], t] == 

    D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara - 

     gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

   V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],

   Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,

   T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0, 

   T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]

share|improve this answer

answered 1 hour ago

user21user21

21k55998

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
  $endgroup$
  – Danial
  12 mins ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
  $endgroup$
  – user21
  11 mins ago
  

  
  
  
  

add a comment | 

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4

$begingroup$

Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:

ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {

   D[V[x, t], 

     t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) + 

     Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

   D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x], 

   D[T[x, t], t] == 

    D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara - 

     gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

   V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],

   Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,

   T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0, 

   T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]

share|improve this answer

answered 1 hour ago

user21user21

21k55998

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
  $endgroup$
  – Danial
  12 mins ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
  $endgroup$
  – user21
  11 mins ago
  

  
  
  
  

add a comment | 

4

$begingroup$

Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:

ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {

   D[V[x, t], 

     t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) + 

     Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

   D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x], 

   D[T[x, t], t] == 

    D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara - 

     gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

   V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],

   Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,

   T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0, 

   T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]

share|improve this answer

answered 1 hour ago

user21user21

21k55998

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you very much. I am using mathematica 11.3, when i use this code in my .nb, its showing errors: General::ivar: 3 is not a valid variable. I need to install different version of mathematica to avoid errors?
  $endgroup$
  – Danial
  12 mins ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Danial, works for me in V11.3. Try quiting your kernel, perhaps?
  $endgroup$
  – user21
  11 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

Here is a version that fixes the syntax errors but there is a warning message indicating instability you should look into:

ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {

   D[V[x, t], 

     t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) + 

     Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

   D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x], 

   D[T[x, t], t] == 

    D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara - 

     gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

   V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],

   Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,

   T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0, 

   T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]

share|improve this answer

answered 1 hour ago

user21user21

21k55998

$endgroup$

ClearAll[V, Rho, T]

gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38;

System = {

   D[V[x, t], 

     t] == -1/gamma/Exp[-x/H]*(D[Rho[x, t], x] + D[T[x, t], x]) + 

     Rho[x, t]/Exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], 

   D[Rho[x, t], t] == -D[Exp[-x/H]*V[x, t], x], 

   D[T[x, t], t] == 

    D[Exp[-x/H]*V[x, t], x] - V[x, t]*Rho[x, t]*gpara - 

     gamma*Exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}],

   V[0, t] == 0, V[1, t] == 0, V[x, 0] == Sin[Pi*x/L],

   Rho[0, t] == 0, Rho[1, t] == 0, Rho[x, 0] == 0,

   T[0, t] == 0, T[1, t] == 0, Derivative[1, 0][T][1, t] == 0, 

   T[x, 0] == 0};

{V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0, 1}, {t, 0, 5}]

Plot3D[{V[x, t], Rho[x, t], T[x, t]}, {x, 0, 1}, {t, 0, 5}]

share|improve this answer

answered 1 hour ago

user21user21

21k55998

answered 1 hour ago

user21user21

21k55998

answered 1 hour ago

user21user21

21k55998