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Discretization of mixed partial deriatives

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Old   June 10, 2004, 05:49
Default Discretization of mixed partial deriatives
  #1
Nasim
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Hello,

I need to solve a partial differential equations having mixed 2nd order partial derivatives like d2u/dxdy.

How can I discretize it in finite difference form?

Is it something like:

(u[i+1][j] - u[i+1][j-1] - u[i][j] + u[i][j-1]) / (2*dx*dy).

Thanks.

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Old   June 14, 2004, 02:55
Default Re: Discretization of mixed partial deriatives
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Rami
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Nasim,

As you wish a 2nd order discretization, a better scheme (assuming a uniform grid) is derived as follows:

U,x|i,j ~ (Ui+1,j - Ui-1,j)/ (2dx)

U,xy|i,j ~ (U,x|i,j),y ~ (Ui+1,j+1 - Ui-1,j+1 - Ui+1,j-1 + Ui-1,j-1) / (4*dx*dy)

Please verify there are no typos. Rami
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