Data commit

Task/Euler-method/Common-Lisp/euler-method-1.lisp

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+;; 't' usually means "true" in CL, but we need 't' here for time/temperature.
+(defconstant true 'cl:t)
+(shadow 't)
+
+
+;; Approximates y(t) in y'(t)=f(t,y) with y(a)=y0 and t=a..b and the step size h.
+(defun euler (f y0 a b h)
+
+  ;; Set the initial values and increments of the iteration variables.
+  (do ((t a  (+ t h))
+       (y y0 (+ y (* h (funcall f t y)))))
+
+      ;; End the iteration when t reaches the end b of the time interval.
+      ((>= t b) 'DONE)
+
+      ;; Print t and y(t) at every step of the do loop.
+      (format true "~6,3F  ~6,3F~%" t y)))
+
+
+;; Example: Newton's cooling law, f(t,T) = -0.07*(T-20)
+(defun newton-cooling (time T) (* -0.07 (- T 20)))
+
+;; Generate the data for all three step sizes (2,5 and 10).
+(euler #'newton-cooling 100 0 100  2)
+(euler #'newton-cooling 100 0 100  5)
+(euler #'newton-cooling 100 0 100 10)

Task/Euler-method/Common-Lisp/euler-method-2.lisp

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+;; slightly more idiomatic Common Lisp version
+
+(defun newton-cooling (time temperature)
+  "Newton's cooling law, f(t,T) = -0.07*(T-20)"
+  (declare (ignore time))
+  (* -0.07 (- temperature 20)))
+
+(defun euler (f y0 a b h)
+  "Euler's Method.
+Approximates y(time) in y'(time)=f(time,y) with y(a)=y0 and t=a..b and the step size h."
+  (loop for time from a below b by h
+        for y = y0 then (+ y (* h (funcall f time y)))
+        do (format t "~6,3F  ~6,3F~%" time y)))