How to solve the given Partial Differential Equation? The 2019 Stack Overflow Developer Survey Results Are InDoes solve PDE by combination of variables always cannot find the general solutions?Separating Partial Differential EqPartial Differential Equation $u_t=3u_xx$How to solve a first order partial differential equation?solving a partial differential equation (Damped heat equation)Solve the following Partial Differential Equation with homogeneous BC'schange of coordinates in partial differential equation (reynolds equation)Write the ODEs of this PDE in Sturm-Liouville form using separation of variablesHow to write the ODEs of a PDE in Sturm-Liouville form, when there are no boundary conditionsDifficult partial differential equation
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How to solve the given Partial Differential Equation?
The 2019 Stack Overflow Developer Survey Results Are InDoes solve PDE by combination of variables always cannot find the general solutions?Separating Partial Differential EqPartial Differential Equation $u_t=3u_xx$How to solve a first order partial differential equation?solving a partial differential equation (Damped heat equation)Solve the following Partial Differential Equation with homogeneous BC'schange of coordinates in partial differential equation (reynolds equation)Write the ODEs of this PDE in Sturm-Liouville form using separation of variablesHow to write the ODEs of a PDE in Sturm-Liouville form, when there are no boundary conditionsDifficult partial differential equation
$begingroup$
I need help on solving the following PDE by Maple or Mathematica:
beginequation
D Big( D - frac1alpha fracpartialpartial t Big) f + fracsinthetaalpha bigg( fracpartial fpartial r fracpartialpartial theta Big(fracDfr^2 sintheta Big) - fracpartial fpartial theta fracpartialpartial r Big(fracDfr^2 sintheta Big) bigg) = 0
endequation
Where $f=f(t,r,theta$) defined in the spherical coordinate and $D$ an operator:
beginequation
D = fracpartial^2partial r^2 + frac1r^2 fracpartial^2partial theta^2 - fraccosthetar^2 sintheta fracpartialpartial theta
endequation
Here is the link that provides you the code written in Maple:
https://www.dropbox.com/s/iej0mpf6z05k6o4/spherical-outputs.mw?dl=0
With the hint of separation of variables $f(t,r,theta)=T(t) cdot R(r) cdot Theta(theta)$, Maple couldn't solve the PDE probably because it is not separatable. Can anyone help me to solve this equation with any method in Maple or Mathematica?
Based on the known solution for more simple case, I also formulated the time-dependency $T(t)=e^-lambda^2 alpha t$ and used the change of variable $f(t,r,theta)=e^-lambda^2 alpha t (r cdot fracpartial g(r,theta)partial r)$, but still couldn't solve it. Does anyone know a change of variables that could potentially solve this kind of PDE?
pde maple change-of-variable
asked Apr 6 at 21:57
AhmadAhmad
262
$endgroup$
add a comment |
$begingroup$
I need help on solving the following PDE by Maple or Mathematica:
beginequation
D Big( D - frac1alpha fracpartialpartial t Big) f + fracsinthetaalpha bigg( fracpartial fpartial r fracpartialpartial theta Big(fracDfr^2 sintheta Big) - fracpartial fpartial theta fracpartialpartial r Big(fracDfr^2 sintheta Big) bigg) = 0
endequation
Where $f=f(t,r,theta$) defined in the spherical coordinate and $D$ an operator:
beginequation
D = fracpartial^2partial r^2 + frac1r^2 fracpartial^2partial theta^2 - fraccosthetar^2 sintheta fracpartialpartial theta
endequation
Here is the link that provides you the code written in Maple:
https://www.dropbox.com/s/iej0mpf6z05k6o4/spherical-outputs.mw?dl=0
With the hint of separation of variables $f(t,r,theta)=T(t) cdot R(r) cdot Theta(theta)$, Maple couldn't solve the PDE probably because it is not separatable. Can anyone help me to solve this equation with any method in Maple or Mathematica?
Based on the known solution for more simple case, I also formulated the time-dependency $T(t)=e^-lambda^2 alpha t$ and used the change of variable $f(t,r,theta)=e^-lambda^2 alpha t (r cdot fracpartial g(r,theta)partial r)$, but still couldn't solve it. Does anyone know a change of variables that could potentially solve this kind of PDE?
pde maple change-of-variable
asked Apr 6 at 21:57
AhmadAhmad
262
$endgroup$
3
$begingroup$
Your PDE doesn't seem to be written correctly: the second D that appears in the formula has no function that it can act upon.
$endgroup$
– Adam Latosiński
Apr 6 at 23:55
$begingroup$
You're right. I've already fixed it. Function $f(t,r,theta)$ is multiplied to both $D$ and $frac1alpha fracpartialpartial t$.
$endgroup$
– Ahmad
Apr 8 at 1:19
add a comment |
$begingroup$
I need help on solving the following PDE by Maple or Mathematica:
beginequation
D Big( D - frac1alpha fracpartialpartial t Big) f + fracsinthetaalpha bigg( fracpartial fpartial r fracpartialpartial theta Big(fracDfr^2 sintheta Big) - fracpartial fpartial theta fracpartialpartial r Big(fracDfr^2 sintheta Big) bigg) = 0
endequation
Where $f=f(t,r,theta$) defined in the spherical coordinate and $D$ an operator:
beginequation
D = fracpartial^2partial r^2 + frac1r^2 fracpartial^2partial theta^2 - fraccosthetar^2 sintheta fracpartialpartial theta
endequation
Here is the link that provides you the code written in Maple:
https://www.dropbox.com/s/iej0mpf6z05k6o4/spherical-outputs.mw?dl=0
With the hint of separation of variables $f(t,r,theta)=T(t) cdot R(r) cdot Theta(theta)$, Maple couldn't solve the PDE probably because it is not separatable. Can anyone help me to solve this equation with any method in Maple or Mathematica?
Based on the known solution for more simple case, I also formulated the time-dependency $T(t)=e^-lambda^2 alpha t$ and used the change of variable $f(t,r,theta)=e^-lambda^2 alpha t (r cdot fracpartial g(r,theta)partial r)$, but still couldn't solve it. Does anyone know a change of variables that could potentially solve this kind of PDE?
pde maple change-of-variable
asked Apr 6 at 21:57
AhmadAhmad
262
$endgroup$
I need help on solving the following PDE by Maple or Mathematica:
beginequation
D Big( D - frac1alpha fracpartialpartial t Big) f + fracsinthetaalpha bigg( fracpartial fpartial r fracpartialpartial theta Big(fracDfr^2 sintheta Big) - fracpartial fpartial theta fracpartialpartial r Big(fracDfr^2 sintheta Big) bigg) = 0
endequation
Where $f=f(t,r,theta$) defined in the spherical coordinate and $D$ an operator:
beginequation
D = fracpartial^2partial r^2 + frac1r^2 fracpartial^2partial theta^2 - fraccosthetar^2 sintheta fracpartialpartial theta
endequation
Here is the link that provides you the code written in Maple:
https://www.dropbox.com/s/iej0mpf6z05k6o4/spherical-outputs.mw?dl=0
With the hint of separation of variables $f(t,r,theta)=T(t) cdot R(r) cdot Theta(theta)$, Maple couldn't solve the PDE probably because it is not separatable. Can anyone help me to solve this equation with any method in Maple or Mathematica?
Based on the known solution for more simple case, I also formulated the time-dependency $T(t)=e^-lambda^2 alpha t$ and used the change of variable $f(t,r,theta)=e^-lambda^2 alpha t (r cdot fracpartial g(r,theta)partial r)$, but still couldn't solve it. Does anyone know a change of variables that could potentially solve this kind of PDE?
pde maple change-of-variable
pde maple change-of-variable
asked Apr 6 at 21:57
AhmadAhmad
262
asked Apr 6 at 21:57
AhmadAhmad
262
edited 2 days ago
Ahmad
asked Apr 6 at 21:57
AhmadAhmad
262
asked Apr 6 at 21:57
AhmadAhmad
262
asked Apr 6 at 21:57
AhmadAhmad
262
262
3
$begingroup$
Your PDE doesn't seem to be written correctly: the second D that appears in the formula has no function that it can act upon.
$endgroup$
– Adam Latosiński
Apr 6 at 23:55
$begingroup$
You're right. I've already fixed it. Function $f(t,r,theta)$ is multiplied to both $D$ and $frac1alpha fracpartialpartial t$.
$endgroup$
– Ahmad
Apr 8 at 1:19
add a comment |
3
$begingroup$
Your PDE doesn't seem to be written correctly: the second D that appears in the formula has no function that it can act upon.
$endgroup$
– Adam Latosiński
Apr 6 at 23:55
$begingroup$
You're right. I've already fixed it. Function $f(t,r,theta)$ is multiplied to both $D$ and $frac1alpha fracpartialpartial t$.
$endgroup$
– Ahmad
Apr 8 at 1:19
3
3
$begingroup$
Your PDE doesn't seem to be written correctly: the second D that appears in the formula has no function that it can act upon.
$endgroup$
– Adam Latosiński
Apr 6 at 23:55
$begingroup$
Your PDE doesn't seem to be written correctly: the second D that appears in the formula has no function that it can act upon.
$endgroup$
– Adam Latosiński
Apr 6 at 23:55
$begingroup$
You're right. I've already fixed it. Function $f(t,r,theta)$ is multiplied to both $D$ and $frac1alpha fracpartialpartial t$.
$endgroup$
– Ahmad
Apr 8 at 1:19
$begingroup$
You're right. I've already fixed it. Function $f(t,r,theta)$ is multiplied to both $D$ and $frac1alpha fracpartialpartial t$.
$endgroup$
– Ahmad
Apr 8 at 1:19
add a comment |
0
active
oldest
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3
$begingroup$
Your PDE doesn't seem to be written correctly: the second D that appears in the formula has no function that it can act upon.
$endgroup$
– Adam Latosiński
Apr 6 at 23:55
$begingroup$
You're right. I've already fixed it. Function $f(t,r,theta)$ is multiplied to both $D$ and $frac1alpha fracpartialpartial t$.
$endgroup$
– Ahmad
Apr 8 at 1:19