This paper by Bengt Fornberg presents a method for generating finite difference formulas on one-dimensional grids with arbitrary spacing. The authors derive simple recursions to calculate the weights for any order of derivative and accuracy, which are particularly useful for dynamically changing grids. The method is more straightforward and less error-prone compared to previous approaches, which were often complex and limited to equidistant grids. The paper includes tables of weights for special cases, such as equispaced grids, up to the 4th derivative and up to 9 weights. The algorithm is described in detail, and the derivation of the recursion relations is provided. The method is applicable to both centered and one-sided approximations at grid points and 'half-way' points. The paper also acknowledges the referee's helpful comments and references several previous works in the field.This paper by Bengt Fornberg presents a method for generating finite difference formulas on one-dimensional grids with arbitrary spacing. The authors derive simple recursions to calculate the weights for any order of derivative and accuracy, which are particularly useful for dynamically changing grids. The method is more straightforward and less error-prone compared to previous approaches, which were often complex and limited to equidistant grids. The paper includes tables of weights for special cases, such as equispaced grids, up to the 4th derivative and up to 9 weights. The algorithm is described in detail, and the derivation of the recursion relations is provided. The method is applicable to both centered and one-sided approximations at grid points and 'half-way' points. The paper also acknowledges the referee's helpful comments and references several previous works in the field.