Finite difference formulas in the complex plane - Fornberg, Bengt (Numerical algorithms, 2022)
Among general functions of two variables f ( x , y ), analytic functions f ( z ) with z = x + i y form a very important special case. One consequence of analyticity turns out to be that 2-D finite difference (FD) formulas can be made remarkably accurate already for small stencil sizes. This article discusses some key properties of such complex plane FD formulas. Application areas include numerical differentiation, interpolation, contour integration, and analytic continuation.