Data update

Task/Euler-method/DuckDB/euler-method.duckdb

@@ -0,0 +1,26 @@
+# Declaration for the sake of euler_table()
+create or replace function cooling(x,y) as NULL;
+
+# Euler method assuming cooling/2 is available
+create or replace function euler_table(x_start, y_start, x2, h) as table (
+  with recursive cte as (
+    select x_start::DOUBLE as x, y_start::DOUBLE as y
+    union all
+    select x + h as x,
+           y + h*cooling(x, y)
+    from cte
+    where (x < x2 and x_start < x2) or
+          (x > x2 and x_start > x2)
+  )
+  from cte
+);
+
+create or replace function euler(x_start, y_start, x2, h) as (
+  select last(y order by x) from euler_method(x_start, y_start, x2, h)
+);
+
+## Example:
+create or replace function cooling(x,y) as
+  -0.07 * (y - 20);
+
+select h, euler(0,100, 100, h) from unnest([1,2,5,10,20]) _(h);

Task/Euler-method/EasyLang/euler-method.easy

@@ -1,23 +1,9 @@
 TR = 20
 K = -0.07
-func analytic T0 t .
-   return TR + (T0 - TR) * pow 2.71828 (K * t)
-.
 ytxt = 95
-proc draw_analytic a b .
-   gcolor 009
-   gtext 80 ytxt "analytic"
-   ytxt -= 5
-   for t = a to b
-      yp = y
-      y = analytic 100 t
-      if t > a : gline t - 1 yp t y
-   .
-.
 drawgrid
 glinewidth 0.3
 gtextsize 3
-draw_analytic 0 100
 #
 func newton_cooling temp .
    return K * (temp - TR)
@@ -26,14 +12,27 @@ proc draw_euler y t t2 step col .
    gcolor col
    gtext 80 ytxt "step: " & step
    ytxt -= 5
-   repeat
+   gpenup
+   while t <= t2
+      glineto t y
       t += step
-      yp = y
       y += step * newton_cooling y
-      gline t - step yp t y
-      until t >= t2
+   .
+.
+func analytic T0 t .
+   return TR + (T0 - TR) * pow 2.71828 (K * t)
+.
+proc draw_analytic a b .
+   gcolor 009
+   gtext 80 ytxt "analytic"
+   ytxt -= 5
+   gpenup
+   for t = a to b
+      y = analytic 100 t
+      glineto t y
    .
 .
 draw_euler 100 0 100 10 900
 draw_euler 100 0 100 5 555
 draw_euler 100 0 100 2 090
+draw_analytic 0 100

Task/Euler-method/FutureBasic/euler-method.basic

@@ -0,0 +1,33 @@
+include "NSLog.incl"
+
+double local fn Cooling( t as double, temp as double )
+  return -0.07 * (temp - 20 )
+end fn = 0.0
+
+void local fn Euler( y as double, stepSize as int, endTime as double )
+  int t = 0
+  NSLog( @"\n  Step %2d: \b", stepSize )
+  while ( t <= endTime )
+    if ( t % 10 == 0 ) then NSLog( @" %7.3f \b", y )
+    y += stepSize * fn Cooling( t, y )
+    t += stepSize
+  wend
+end fn
+
+void local fn Analytic
+  NSLog( @"    Time: \b" )
+  for int t1 = 0 to 100 step 10
+    NSLog( @" %8d\b", t1 )
+  next
+  NSLog( @"\nAnalytic: \b" )
+  for int t2 = 0 to 100 step 10
+    NSLog( @"%9.3f\b", 20 + 80 * exp(-0.07 * t2 ) )
+  next
+end fn
+
+fn Analytic
+fn Euler( 100.0,  2.0, 100.0 )
+fn Euler( 100.0,  5.0, 100.0 )
+fn Euler( 100.0, 10.0, 100.0 )
+
+HandleEvents

Task/Euler-method/Pluto/euler-method.pluto

@@ -0,0 +1,25 @@
+local fmt = require "fmt"
+
+local function euler(f, y, step, finish)
+    fmt.write(" Step %2d: ", step)
+    for t = 0, finish, step do
+        if t % 10 == 0 then fmt.write(" %7.3f", y) end
+        y += step * f(y)
+    end
+    print()
+end
+
+local function analytic()
+    io.write("    Time: ")
+    for t = 0, 100, 10 do fmt.write(" %7d", t) end
+    io.write("\nAnalytic: ")
+    for t = 0, 100, 10 do
+        fmt.write(" %7.3f", 20 + 80 * math.exp(-0.07 * t))
+    end
+    print()
+end
+
+local cooling = |temp| -> -0.07 * (temp - 20)
+
+analytic()
+for {2, 5, 10} as i do euler(cooling, 100, i, 100) end