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
asked 2 hours ago
Danial Danial
62
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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
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.
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add a comment |
1
1
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
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.
$endgroup$
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
differential-equations
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.
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edited 2 hours ago
Danial
asked 2 hours ago
Danial Danial
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asked 2 hours ago
Danial Danial
62
asked 2 hours ago
Danial Danial
62
62
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Danial is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
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1 Answer
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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}]
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
14 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 mins ago
add a comment |
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1 Answer
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active
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votes
1 Answer
1
active
oldest
votes
active
oldest
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oldest
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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}]
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
14 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 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}]
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
14 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 mins ago
add a comment |
4
4
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}]
answered 1 hour ago
user21user21
21k55998
$endgroup$
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}]
answered 1 hour ago
user21user21
21k55998
answered 1 hour ago
user21user21
21k55998
answered 1 hour ago
user21user21
21k55998
answered 1 hour ago
user21user21
21k55998
21k55998
$begingroup$
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
14 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 mins ago
add a comment |
$begingroup$
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
14 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 mins ago
$begingroup$
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
14 mins ago
$begingroup$
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
14 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 mins ago
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
13 mins ago
add a comment |
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