Errors in solving coupled pdesErrors Solving Elliptic PDES with FEMCoupled elliptic pdes, FEM solverSolving a system of partial differential and algebraic equations? setting the step-size to get reasonable resultsSolving a coupled PDEs using FEM with Robin conditionsSolving coupled ODEsNDSolve for Coupled Second Order PDEsSolving non-linear PDEsSolving coupled pdeNumerically solving two coupled nonlinear PDEsSolving 3 nonlinear, transient, coupled PDEs
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Errors in solving coupled pdes
Errors Solving Elliptic PDES with FEMCoupled elliptic pdes, FEM solverSolving a system of partial differential and algebraic equations? setting the step-size to get reasonable resultsSolving a coupled PDEs using FEM with Robin conditionsSolving coupled ODEsNDSolve for Coupled Second Order PDEsSolving non-linear PDEsSolving coupled pdeNumerically solving two coupled nonlinear PDEsSolving 3 nonlinear, transient, coupled PDEs
2
$begingroup$
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 Apr 24 at 4:23
Danial Danial
163
$endgroup$
add a comment |
2
$begingroup$
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 Apr 24 at 4:23
Danial Danial
163
$endgroup$
add a comment |
2
2
2
$begingroup$
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 Apr 24 at 4:23
Danial Danial
163
$endgroup$
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 Apr 24 at 4:23
Danial Danial
163
asked Apr 24 at 4:23
Danial Danial
163
edited Apr 24 at 4:43
Danial
asked Apr 24 at 4:23
Danial Danial
163
asked Apr 24 at 4:23
Danial Danial
163
asked Apr 24 at 4:23
Danial Danial
163
163
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
5
$begingroup$
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 Apr 24 at 5:36
user21user21
21.4k561101
$endgroup$
$begingroup$
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
Apr 24 at 6:44
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
@Danial, I am not sure I understand your question, do you mean viaNDEigensystem? If so, that is a different question and you should ask a new one.
$endgroup$
– user21
Apr 25 at 7:05
|
show 1 more comment
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
5
$begingroup$
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 Apr 24 at 5:36
user21user21
21.4k561101
$endgroup$
$begingroup$
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
Apr 24 at 6:44
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
@Danial, I am not sure I understand your question, do you mean viaNDEigensystem? If so, that is a different question and you should ask a new one.
$endgroup$
– user21
Apr 25 at 7:05
|
show 1 more comment
5
$begingroup$
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 Apr 24 at 5:36
user21user21
21.4k561101
$endgroup$
$begingroup$
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
Apr 24 at 6:44
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
@Danial, I am not sure I understand your question, do you mean viaNDEigensystem? If so, that is a different question and you should ask a new one.
$endgroup$
– user21
Apr 25 at 7:05
|
show 1 more comment
5
5
5
$begingroup$
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 Apr 24 at 5:36
user21user21
21.4k561101
$endgroup$
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 Apr 24 at 5:36
user21user21
21.4k561101
answered Apr 24 at 5:36
user21user21
21.4k561101
answered Apr 24 at 5:36
user21user21
21.4k561101
answered Apr 24 at 5:36
user21user21
21.4k561101
21.4k561101
$begingroup$
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
Apr 24 at 6:44
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
@Danial, I am not sure I understand your question, do you mean viaNDEigensystem? If so, that is a different question and you should ask a new one.
$endgroup$
– user21
Apr 25 at 7:05
|
show 1 more 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
Apr 24 at 6:44
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
@Danial, I am not sure I understand your question, do you mean viaNDEigensystem? If so, that is a different question and you should ask a new one.
$endgroup$
– user21
Apr 25 at 7:05
$begingroup$
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
Apr 24 at 6:44
$begingroup$
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
Apr 24 at 6:44
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
@Danial, works for me in V11.3. Try quiting your kernel, perhaps?
$endgroup$
– user21
Apr 24 at 6:45
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Thanks @user21, its works after quiting kernel.
$endgroup$
– Danial
Apr 25 at 6:32
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
Can you please suggest me how to get eigen values of this system of equations if i change d/dt =i lambda ?
$endgroup$
– Danial
Apr 25 at 6:35
$begingroup$
@Danial, I am not sure I understand your question, do you mean via
NDEigensystem? If so, that is a different question and you should ask a new one.$endgroup$
– user21
Apr 25 at 7:05
$begingroup$
@Danial, I am not sure I understand your question, do you mean via
NDEigensystem? If so, that is a different question and you should ask a new one.$endgroup$
– user21
Apr 25 at 7:05
|
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