Forward euler implementation in Common Lisp (#607)

Author: Trashtalk217

contents/forward_euler_method/code/clisp/euler.lisp

@@ -0,0 +1,29 @@
+;;;; Forward euler implementation in Common Lisp
+
+(defun solve-euler (timestep n)
+  "Returns a function where y'(t) = -3t and y(0) = 0 using the forward euler method"
+  (loop
+    with result = (make-array n :initial-element 1)
+    for i from 1 upto (1- n) do
+    (setf (svref result i) (- (svref result (1- i)) (* 3 (svref result (1- i)) timestep)))
+    finally (return result)))
+
+(defun approximatep (result threshold timestep)
+  "Checks the result from the solve-euler function"
+  (loop
+    with approximatep = t
+    with solution = 0
+    for i from 0 upto (1- (length result)) do
+    (setf solution (exp (* (- 3) i timestep)))
+    (when (> (- (svref result i) solution) threshold)
+      (setf approximatep nil)
+      (format t "~d ~d~%" (svref result i) solution))
+    finally (return approximatep)))
+
+(defvar timestep 0.01)
+(defvar n 100) ; number of steps
+(defvar threshold 0.01)
+
+(defvar result (solve-euler timestep n))
+(defvar approximatep (approximatep result threshold timestep))
+(format t "~:[Value(s) not in threshold~;All values within threshold~]~%" approximatep)

contents/forward_euler_method/forward_euler_method.md

@@ -144,6 +144,8 @@ Full code for the visualization follows:
 [import, lang:"java"](code/java/ForwardEuler.java)
 {% sample lang="nim" %}
 [import, lang:"nim"](code/nim/forwardeuler.nim)
+{% sample lang="lisp" %}
+[import, lang="lisp"](code/clisp/euler.lisp)
 {% endmethod %}
 
 <script>