An “implicit” method for numerically estimating the derivatives of data on a grid using coefficient templates spanning a more compact range of grid points than the conventional “explicit” differencing template at the same order of accuracy. For example, conventional fourth-order differencing on a uniform grid uses a centered template spanning five values of data; compact fourth-order differencing uses two three-point centered templates, one for the given data and one for the gridded derivatives themselves, which therefore must be solved for simultaneously. The superior accuracy of compact schemes makes them computationally advantageous, provided that the grid geometry is sufficiently regular.