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Using scipy's odeint to solve pde

0

$begingroup$

I would like to use scipy's odeint to solve the following pde:

$$frac 1 r frac partial u partial r + frac partial^2 u partial r^2=frac 1 c_h frac partial u partial t$$

Where $c_h$ is a constant and $u$ is a function of $r$ and $t$. The boundary conditions are:

$u=u_0$ for $r=dfracd_w2$

and,

$dfrac partial h partial r = 0$ for $r=dfracD2$

odeint1 following their basic example only solves n-order ODE's, so I guess the first step is to rewrite my pde as a system of odes. Is separation of variables the way to go here? How can I rewrite the above as two systems of ODE's such that I can plug in to odeint? Also once I get the solution to the two ODE's how can I recombine to get $u(r,t)$?

pde numerical-methods python

share|cite|improve this question

edited Apr 2 at 9:54

Max

1,0021319

asked Apr 2 at 9:30

user32882user32882

391114

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What do you know about converting PDE's to ODE's? Your aim is to use odeint for solving the ODEs, but as you say before you can do this you need suitable ODE's first. Show your research & what you have found in your question.
  $endgroup$
  – unseen_rider
  Apr 2 at 11:44
  

  
  
  
  

add a comment | 

0

$begingroup$

I would like to use scipy's odeint to solve the following pde:

$$frac 1 r frac partial u partial r + frac partial^2 u partial r^2=frac 1 c_h frac partial u partial t$$

Where $c_h$ is a constant and $u$ is a function of $r$ and $t$. The boundary conditions are:

$u=u_0$ for $r=dfracd_w2$

and,

$dfrac partial h partial r = 0$ for $r=dfracD2$

odeint1 following their basic example only solves n-order ODE's, so I guess the first step is to rewrite my pde as a system of odes. Is separation of variables the way to go here? How can I rewrite the above as two systems of ODE's such that I can plug in to odeint? Also once I get the solution to the two ODE's how can I recombine to get $u(r,t)$?

pde numerical-methods python

share|cite|improve this question

edited Apr 2 at 9:54

Max

1,0021319

asked Apr 2 at 9:30

user32882user32882

391114

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What do you know about converting PDE's to ODE's? Your aim is to use odeint for solving the ODEs, but as you say before you can do this you need suitable ODE's first. Show your research & what you have found in your question.
  $endgroup$
  – unseen_rider
  Apr 2 at 11:44
  

  
  
  
  

add a comment | 

$begingroup$

I would like to use scipy's odeint to solve the following pde:

$$frac 1 r frac partial u partial r + frac partial^2 u partial r^2=frac 1 c_h frac partial u partial t$$

Where $c_h$ is a constant and $u$ is a function of $r$ and $t$. The boundary conditions are:

$u=u_0$ for $r=dfracd_w2$

and,

$dfrac partial h partial r = 0$ for $r=dfracD2$

odeint1 following their basic example only solves n-order ODE's, so I guess the first step is to rewrite my pde as a system of odes. Is separation of variables the way to go here? How can I rewrite the above as two systems of ODE's such that I can plug in to odeint? Also once I get the solution to the two ODE's how can I recombine to get $u(r,t)$?

pde numerical-methods python

share|cite|improve this question

edited Apr 2 at 9:54

Max

1,0021319

asked Apr 2 at 9:30

user32882user32882

391114

$endgroup$

share|cite|improve this question

edited Apr 2 at 9:54

Max

1,0021319

asked Apr 2 at 9:30

user32882user32882

391114

share|cite|improve this question

edited Apr 2 at 9:54

Max

1,0021319

asked Apr 2 at 9:30

user32882user32882

391114

edited Apr 2 at 9:54

Max

1,0021319

edited Apr 2 at 9:54

Max

1,0021319

asked Apr 2 at 9:30

user32882user32882

391114

asked Apr 2 at 9:30

user32882user32882

391114