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I am looking for textbook references that describe lattice numerical methods for arbitrary elliptic PDEs, particularly finite difference schemes and particularly in 2d. The few references that I have looked at only treat the laplacian or the heat equation, I would like the more general case when the differential operator does not have constant coefficients, ie $$ Lu = A(x,y) u_{xx} + B(x,y) u_{xy} + C(x,y) u_{yy}. $$

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I know this is a little late, but in the book "Linear and Quasilinear Equations of Parabolic Type" by Ladyzenskaja, Solonnikov and Ural'ceva, finite difference methods are shown for general enough parabolic equations (the elliptic case is subsumed in their explanation too).

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