Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.soft-sys.math.mathematica > #2556 > unrolled thread

Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables

Back to article view | Back to comp.soft-sys.math.mathematica

Contents

  Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables Dan Dubin <ddubin@ucsd.edu> - 2011-05-21 10:46 +0000

#2556 — Re: NDSolve with NIntegrate for a PDE where the unknown function is integrated wrt its variables

>Hello, i know that this issue has been raised many times, but i cannot
>find an answer in the previous posts.
>
>I tried to reformulate my problem in a simple way:
>
>NDSolve[{Derivative[0, 1][Yg][r, t]==NIntegrate[A[r1] Yg[r1, t] , {r1,
>1, r}] + B[r]/Yg[r, t], Yg[r, 0] == r}, {Yg}, {r, 1, 10}, {t, 0, 0.3}]
>
>where A and B are some functions, for example:
>
>A[r_] = r^-1; B[r_] = r + 10;
>
>Please help!

I think you need to do a little math to get this integro-differential 
equation into shape. One simple approach -- take the derivative of 
your equation with respect to r. That turns it into a PDE, first 
order in both r and t. Then I would solve it by finite-differencing 
the PDE on a grid in r.  An extra boundary condition needs to be 
specified then, Derivative[0, 1][Yg][0, t] == B[0]/Yg[0, t] . Second 
approach -- simply finite-difference the original equation in r -- 
write the integral as a sum over the grid using Simpson's rule, for 
instance. In both cases, note that you are solving many coupled ODEs 
in time  for Yg at different grid points. NDSolve should be able to 
handle that even though the ODEs are nonlinear.

-- 
---------------
| Professor Dan Dubin
| Dept of Physics , Mayer Hall Rm 3126,
| UC San Diego La Jolla CA 92093-0319
| phone (858) - 534-4174 fax: (858)-534-0173
| ddubin@ucsd.edu

[toc] | [standalone]

Back to top | Article view | comp.soft-sys.math.mathematica

csiph-web