A-M baby

Task/Euler-method/J/euler-method-1.j

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+NB.*euler a Approximates Y(t) in Y'(t)=f(t,Y) with Y(a)=Y0 and t=a..b and step size h.
+euler=: adverb define
+ 'Y0 a b h'=. 4{. y
+ t=. i.@>:&.(%&h) b - a
+ Y=. (+ h * u)^:(<#t) Y0
+ t,.Y
+)
+
+ncl=: _0.07 * -&20  NB. Newton's Cooling Law

Task/Euler-method/J/euler-method-2.j

@@ -0,0 +1,16 @@
+   ncl euler 100 0 100 2
+...                       NB. output redacted for brevity
+   ncl euler 100 0 100 5
+...                       NB. output redacted for brevity
+   ncl euler 100 0 100 10
+  0     100
+ 10      44
+ 20    27.2
+ 30   22.16
+ 40  20.648
+ 50 20.1944
+ 60 20.0583
+ 70 20.0175
+ 80 20.0052
+ 90 20.0016
+100 20.0005