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Math Help - vector calculus and partial diff

  1. #1
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    vector calculus and partial diff

    I was hoping to get help on the following problems. Hope to c a rpl soon from somebody
    Attached Files Attached Files
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  2. #2
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    Quote Originally Posted by prasoonmishra View Post
    I was hoping to get help on the following problems. Hope to c a rpl soon from somebody
    Why dont you simply post your questions on the forum?
    Many of us object to opening attachements.
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  3. #3
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    i could not write the equation and laplacian operator so i had to attach the file...
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  4. #4
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    Quote Originally Posted by prasoonmishra View Post
    i could not write the equation and laplacian operator so i had to attach the file...
    It is clearly in Latex.
    [tex]\nabla[/tex] gives \nabla.
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  5. #5
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    Hint: Some of the possible solutions to these problems involve using Lanczos iteration, so make sure you are familiar with this algorithm.

    Hint: I highly recommend that you avoid trying to solve for the eigenvalues of a non-hermetian matrix in any of the following problems. If your approach requires this, consider doing something else.

    1. Consider a box with length, width and height given by L. The box encompasses the region described by 0<=x<=L, 0<=y<=L, and 0<=z<=L. A scalar field inside the box satisfies the differential equation:
    \nabla^2\Psi=-a\Psi (1)

    Note that the differential operator here is known as the Laplacian. An equivalent of writing the equation is:

    \Delta\Psi=-a\Psi (2)

    Here a is a positive constant that is equal to 30/L^2.

    The field is 0 on the surfaces y=0, y=L, x=0, x=L and finally the surface z=L. On the surface z=0, the field has the functional form:

     \Psi(x,y)=(1-|x-\frac{L}{2}|\frac{2}{L})(1-|y-\frac{L}{2}|\frac{2}{L}) (3)

    Solve for y as a function of x, y, and z inside the box. Your final solution must be an analytic expression, though it can involve an infinite sum.


    2. Consider the system of nonlinear partial differential equations:

    \partial f/ \partial x=\partial g/ \partial y +af^2

    \partial f/ \partial y = \partial g/ \partial x (1)

    Here a is a small positive constant, such that a <<1. The boundary conditions are:

     f(x,0)= \sin(\frac{\pi}{L} 100x) (2)

     f(0,y)=0 (3)
     f(L,y)=0 (4)
     g(x,0)=0 (5)

    Solve for f(x,y) and g(x,y) for 0<=x<=L and y>=0 to first order in a. Your solution should be a finite sum of elementary functions. Numerical approximations are not to be used.
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  6. #6
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    Now i have posted the question directly. Look into the questions please...
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