• Re: Solving a nonlinear elliptic PDE numerically with Matlab.

    From Francesco Chiodo@21:1/5 to All on Fri Sep 24 10:21:40 2021
    Il giorno lunedì 24 agosto 2015 alle 14:36:20 UTC+2 Alan Weiss ha scritto:
    On 8/23/2015 10:36 AM, Alan Ray wrote:
    "Nasser M. Abbasi" wrote in message <mrckbp$1fm$1...@speranza.aioe.org>...
    On 8/23/2015 7:12 AM, Alan Ray wrote:
    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. >> >

    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"

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

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