Solving a nonlinear elliptic PDE numerically with Matlab.

[Alan Ray]

Hi I wish to solve numerically the following boundary condition PDE problem:

u_{xx}+u_{yy} = \sqrt{u} + (u_x)^2/u^{3/2}

with BCS: u(0, y) = 1, D[1](u)(1, y) = 0, u(x, 0) = 1, D[2](u)(x, 0) = 0

Is there a routine or script in Matlab which is ready to be used for the above problem, or do I need to write my own script, which I am a bit weak in programming.

And I don't know of any nonlinear methods that I can use for this PDE.

[Nasser M. Abbasi]

if you have the pde toolbox you can try

http://www.mathworks.com/help/pde/index.html
http://www.mathworks.com/help/pde/ug/pdenonlin.html

"[u,res] = pdenonlin(model,c,a,f) solves the nonlinear scalar PDE problem"

[Alan Ray]

"Nasser M. Abbasi" wrote in message <mrckbp$1fm$1...@speranza.aioe.org>...

How do I use pdenonlin in my pde?
I just see that it's used in one case of minimal surfaces, how to use it in my case?

[Alan Weiss]

There is a bit of a learning curve with PDE Toolbox. I suggest that you
open the PDE app by entering
pdetool
at the command line (I assume that you have a PDE Toolbox license). Then
draw your geometry, which I think is a square from (0,0) to (1,1). I
suggest that you use the Snap option.

Then set the boundary conditions by entering Boundary Mode,
double-clicking the edges one at a time, and entering your boundary
conditions. For the Dirichlet conditions set h = 1 and r to be the value
(the description of the equation is in the dialog box). For the Neumann
condition, the default q = 0 and g = 0 will do.

To get a nonlinear solver, from the Solve > Parameters menu, choose the
nonlinear solver. You will have to figure out how to input the
coefficients for your problem, too, but that should be straightforward.
Hint: c = 1, a = 0, but f contains your nonlinear function. Make sure
you get the sign correct!

The documentation should help.

Good luck,

Alan Weiss
MATLAB mathematical toolbox documentation

[Francesco Chiodo]

Hi, i would like to know how to have a number solution from this elliptic equation:
E[2*pi*a; -h^2*pi^2]