Take the 2-minute tour ×
Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. It's 100% free, no registration required.

I need some hints on how to solve this diffusion equation ($\alpha, k_1,k_2$ and $k_3$ are constants):

$$ {\partial P \over \partial y} + k_1 {\partial P \over \partial t} + \alpha P = {1 \over k_2} {1 \over x}{\partial \over \partial x} \left(x k_3 {\partial P \over \partial x}\right) $$

With boundary conditions:
$P(x=1,y,t)=0$
$k_3 {\partial P \over \partial x}|_{x=0}=0$
$P(x,0,t)=p(x)$

I've been told that DuFort-Frankel is a proper method for this example, so I tried (not sure if it is correct):

$${P_{i,j+1}^n-P_{i,j-1}^n \over 2 \Delta y}+k_1{P_{i,j}^{n+1}-P_{i,j}^{n-1} \over 2 \Delta t}+\alpha P_{i,j}^n = {k_3 \over k_2x}\left({P_{i+1,j}^n-P_{i-1,j}^n \over 2 \Delta x}+x{P_{i+1,j}^n-(P_{i,j}^{n+1}+P_{i,j}^{n-1})+P_{i-1,j}^n \over \Delta x^2}\right)$$

But I don't know how tie this with boundary conditions so I can solve it using recursive functions... It is supposed to be pretty easy, am I missing something? DuFort-Frankel is not necessary, if You know how to solve it using Taylor, Leapfrog, Richardson or any other method, I would be very grateful for any hints...

share|improve this question
    
You may want to express $x$ in terms of $i$ (I assume that $i$ is a horizontal, while $j$ is a vertical lattice point). –  rlgordonma Jan 10 '13 at 21:48
    
You mean I should use $i \Delta x$ instead of $x$? Still cannot figure out how to make use of the boundary conditions... –  apm Jan 10 '13 at 23:18
    
Yes, that's what I mean. –  rlgordonma Jan 10 '13 at 23:31
add comment

migrated from math.stackexchange.com Jan 23 '13 at 0:06

This question came from our site for people studying math at any level and professionals in related fields.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.