Another update from ingydotnet^djgoku

Task/Euler-method/BASIC/euler-method-1.basic

@@ -0,0 +1,15 @@
+      PROCeuler("-0.07*(y-20)", 100, 0, 100, 2)
+      PROCeuler("-0.07*(y-20)", 100, 0, 100, 5)
+      PROCeuler("-0.07*(y-20)", 100, 0, 100, 10)
+      END
+
+      DEF PROCeuler(df$, y, a, b, s)
+      LOCAL t, @%
+      @% = &2030A
+      t = a
+      WHILE t <= b
+        PRINT t, y
+        y += s * EVAL(df$)
+        t += s
+      ENDWHILE
+      ENDPROC

Task/Euler-method/BASIC/euler-method-2.basic

@@ -0,0 +1,24 @@
+'Freebasic .9
+'Custom rounding
+#define round(x,N) Rtrim(Rtrim(Left(Str((x)+(.5*Sgn((x)))/(10^(N))),Instr(Str((x)+(.5*Sgn((x)))/(10^(N))),".")+(N)),"0"),".")
+
+#macro Euler(fn,_y,min,max,h,printoption)
+Print "Step ";#h;":":Print
+Print "time","Euler"," Analytic"
+If printoption<>"print" Then Print "Data omitted ..."
+Scope
+    Dim As Double temp=(min),y=(_y)
+    Do
+        If printoption="print" Then Print temp,round(y,3),20+80*Exp(-0.07*temp)
+        y=y+(h)*(fn)
+        temp=temp+(h)
+    Loop Until temp>(max)
+    Print"________________"
+    Print
+End Scope
+#endmacro
+
+Euler(-.07*(y-20),100,0,100,2,"don't print")
+Euler(-.07*(y-20),100,0,100,5,"print")
+Euler(-.07*(y-20),100,0,100,10,"print")
+Sleep

Task/Euler-method/BASIC/euler-method-3.basic

@@ -0,0 +1,14 @@
+x = euler(-0.07,-20, 100, 0, 100, 2)
+x = euler-0.07,-20, 100, 0, 100, 5)
+x = euler(-0.07,-20, 100, 0, 100, 10)
+end
+
+FUNCTION euler(da,db, y, a, b, s)
+print "===== da:";da;" db:";db;" y:";y;" a:";a;" b:";b;" s:";s;" ==================="
+t = a
+WHILE t <= b
+   PRINT t;chr$(9);y
+   y = y + s * (da * (y + db))
+   t = t + s
+WEND
+END FUNCTION

Task/Euler-method/Elixir/euler-method.elixir

@@ -0,0 +1,13 @@
+defmodule Euler do
+  def method(_, _, t, b, _) when t>b, do: :ok
+  def method(f, y, t, b, h) do
+    :io.format "~7.3f ~7.3f~n", [t,y]
+    method(f, y + h * f.(t,y), t + h, b, h)
+  end
+end
+
+f = fn _time, temp -> -0.07 * (temp - 20) end
+Enum.each([10, 5, 2], fn step ->
+  IO.puts "\nStep = #{step}"
+  Euler.method(f, 100.0, 0.0, 100.0, step)
+end)

Task/Euler-method/Julia/euler-method.julia

@@ -0,0 +1,16 @@
+euler(f,T,t0,t1,h)=[(T,T+=h*f(T))[1] for t=t0:h:t1]
+
+# Prints a series of arbitrary values in a tabular form, left aligned in cells with a given width
+tabular(width,cells...)=println(join(map(s->rpad(s,width),cells),""))
+
+# prints the table according to the task description for h=5 and 10 sec
+for h=(5,10)
+print("Step $h:\n\n")
+tabular(15,"Time","Euler","Analytic")
+t=0
+for T=euler(y->-0.07*(y-20.0),100.0,0,100,h)
+tabular(15,t,round(T,6),round(20.0+80.0*exp(-0.07*t),6))
+t+=h
+end
+println()
+end

Task/Euler-method/PowerShell/euler-method.psh

@@ -0,0 +1,43 @@
+function euler (${f}, ${y}, $y0, $t0, $tEnd) {
+    function f-euler ($tn, $yn, $h)  {
+        $yn + $h*(f $tn $yn)
+    }
+    function time ($t0, $h, $tEnd)  {
+        $end = [MATH]::Floor(($tEnd - $t0)/$h)
+        foreach ($_ in 0..$end) { $_*$h + $t0 }
+    }
+    $time = time $t0 10 $tEnd
+    $time5 = time $t0 5 $tEnd
+    $time2 = time $t0 2 $tEnd
+    $yn10 = $yn5 = $yn2 = $y0
+    $i2 = $i5 = 0
+    foreach ($tn10 in $time) {
+        while($time2[$i2] -ne $tn10) {
+            $i2++
+            $yn2 = (f-euler $time2[$i2] $yn2 2)
+        }
+        while($time5[$i5] -ne $tn10) {
+            $i5++
+            $yn5 = (f-euler $time5[$i5] $yn5 5)
+        }
+        [pscustomobject]@{
+            t = "$tn10"
+            Analytical = "$("{0:N5}" -f (y $tn10))"
+            "Euler h = 2" = "$("{0:N5}" -f $yn2)"
+            "Euler h = 5" = "$("{0:N5}" -f $yn5)"
+            "Euler h = 10" = "$("{0:N5}" -f $yn10)"
+            "Error h = 2" = "$("{0:N5}" -f [MATH]::abs($yn2 - (y $tn10)))"
+            "Error h = 5" = "$("{0:N5}" -f [MATH]::abs($yn5 - (y $tn10)))"
+            "Error h = 10" = "$("{0:N5}" -f [MATH]::abs($yn10 - (y $tn10)))"
+        }
+        $yn10 = (f-euler $tn10 $yn10 10)
+    }
+}
+$k, $yr, $y0, $t0, $tEnd = 0.07, 20, 100, 0, 100
+function f ($t, $y)  {
+    -$k *($y - $yr)
+}
+function y ($t)  {
+    $yr + ($y0 - $yr)*[MATH]::Exp(-$k*$t)
+}
+euler f y $y0 $t0 $tEnd | Format-Table -AutoSize

Task/Euler-method/Python/euler-method.py

@@ -1,6 +1,6 @@
 def euler(f,y0,a,b,h):
 	t,y = a,y0
-	while t < b:
+	while t <= b:
 		print "%6.3f %6.3f" % (t,y)
 		t += h
 		y += h * f(t,y)

Task/Euler-method/REXX/euler-method.rexx

@@ -51,3 +51,22 @@ o:
   Parse Arg v
   Say right(t,3) format(Tr+(T0-Tr)/exp(k*t),5,10) format(v,5,10)
   Return
+
+exp: Procedure
+  Parse Arg x,prec
+  If prec<9 Then prec=9
+  Numeric Digits (2*prec)
+  Numeric Fuzz   3
+  o=1
+  u=1
+  r=1
+  Do i=1 By 1
+    ra=r
+    o=o*x
+    u=u*i
+    r=r+(o/u)
+    If r=ra Then Leave
+    End
+  Numeric Digits (prec)
+  r=r+0
+  Return r