Finite Difference for Laplace Operators

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 May 17, 2016, 07:16 Finite Difference for Laplace Operators #1 New Member   Join Date: Feb 2016 Posts: 14 Rep Power: 3 Hi, I am working on the finite volume method on a clustered Cartesian grid for school. I am using a finite difference function I made previously to get the operators for u,v,d u/v d x/y for solving the Poisson equation. The function evaluates the taylor expansion for each point of stencil x of phi about x0 and returns the coefficient matrix [phi^0] [phi_i-1] [phi^1] = A* [phi_i ] [phi^2] [phi_i+1] I am looking for the zeroth derivative of the phi as I am trying to use this to interpolate the value itself. How do I go about this? I have the values of phi on other points, but not on x0 itself. Any help would be great

 May 17, 2016, 11:06 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,564 Rep Power: 40 the zeroth derivative of phi in x0 is phi(i) ... f(i+1) -f(i) = h* df/dx|i + h^2/2*d2f/dx^2|i + ... f(i+1)-f(i) = -h* df/dx|i + h^2/2*d2f/dx^2|i deltaf = A * derivatives + hot -> derivatives = A^-1*deltaf - A^-1*hot A is 2x2. Then, you disregard A^-1*hot and you get the vector derivatives_n which approximates the exact derivative

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