NDSolve`FiniteDifferenceDerivative is a very helpful function to calculate numerical derivatives. It is explained in the tutorial The Numerical Method of Lines in more detail.

Here I found the reference BENGT FORNBERG:CALCULATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS which explains how the weights are to be calculated in the one dimensional case.

I couldn't find a similar reference for the two dimensional case.

My question:

• How is the differentiation matrix evaluated in this case, especially at boundary meshpoints?
• Are there additional helpful references in the Mathematica documentation?

Thanks!