fdm.rkt

Finite difference methods for estimating derivatives in Racket. The API is loosely based on that of fdm and FiniteDifferences.jl (née FDM.jl). This package provides a small subset of the functionality provided by those.

API

(forward-grid p)
(backward-grid p)
(central-grid p)

These functions define the grids for a forward, backward, or central finite difference method of order p.

(dfdx g p q f x
      #:adapt
      #:condition
      #:eps
      #:bound)

Compute the qth derivative of the univariate, real-valued function f at x using a finite difference method of order p with a grid defined by g. g should be one of the aforementioned functions. The keyword arguments are:

• adapt: The number of adaptive steps to use to improve the estimate of bound. Defaults to 1. Set to 0 to disable adaptive bound computation.
• condition: The condition number used when computing bounds. Defaults to 100.
• eps: The assumed roundoff error. Defaults to epsilon.0.
• bound: Bound on the value of the function f and its derivatives at x. This value is computed and should not generally need to be specified.