;;; Copyright © 2021 Gerald Sussman and Chris Hanson
;;; Copyright © 2022 David Thompson <dthompson2@worcester.edu>
;;;
;;; This program is free software: you can redistribute it and/or
;;; modify it under the terms of the GNU General Public License as
;;; published by the Free Software Foundation, either version 3 of the
;;; License, or (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program.  If not, see
;;; <http://www.gnu.org/licenses/>.

(define (stormer-2 F h)
  (lambda (history)
    (+ (* 2 (x 0 history))
       (* -1 (x 1 history))
       (* (/ (expt h 2) 12)
          (+ (* 13 (F (t 0 history) (x 0 history)))
             (* -2 (F (t 1 history) (x 1 history)))
             (F (t 2 history) (x 2 history)))))))

(define (stepper h integrator)
  (lambda (history)
    (extend-history (+ (t 0 history) h)
                    (integrator history)
                    history)))

(define n:> >)
(define n:- -)

(define (evolver F h make-integrator)
  (let* ((integrator (make-integrator F h))
         (step (stepper h integrator)))
    (define (evolve history n-steps)
      (if (n:> n-steps 0)
          (evolve (step history) (n:- n-steps 1))
          history))
    evolve))