langs a-z

Task/Euler-method/Objeck/euler-method.objeck

@@ -0,0 +1,32 @@
+class EulerMethod {
+  T0 : static : Float;
+  TR : static : Float;
+  k : static : Float;
+  delta_t : static : Float[];
+  n : static : Float;
+
+  function : Main(args : String[]) ~ Nil {
+    T0 := 100;
+    TR := 20;
+    k := 0.07;
+    delta_t := [2.0, 5.0, 10.0];
+    n := 100;
+
+    f := NewtonCooling(Float) ~ Float;
+    for(i := 0; i < delta_t->Size(); i+=1;) {
+      IO.Console->Print("delta_t = ")->PrintLine(delta_t[i]);
+      Euler(f, T0, n->As(Int), delta_t[i]);
+    };
+  }
+
+  function : native : NewtonCooling(t : Float) ~ Float {
+    return -1 * k * (t-TR);
+  }
+
+  function : native : Euler(f : (Float) ~ Float, y : Float, n : Int, h : Float) ~ Nil {
+    for(x := 0; x<=n; x+=h;) {
+      IO.Console->Print("\t")->Print(x)->Print("\t")->PrintLine(y);
+      y += h * f(y);
+    };
+  }
+}

Task/Euler-method/PL-I/euler-method.pli

@@ -0,0 +1,44 @@
+test: procedure options (main); /* 3 December 2012 */
+
+   declare (x, y, z) float;
+   declare (T0 initial (100), Tr initial (20)) float;
+   declare k float initial (0.07);
+   declare t fixed binary;
+   declare h fixed binary;
+
+   x, y, z = T0;
+   /* Step size is 2 seconds */
+   h = 2;
+   put skip data (h);
+   put skip list ('  t    By formula', 'By Euler');
+   do t = 0 to 100 by 2;
+      put skip edit (t, Tr + (T0 - Tr)/exp(k*t), x) (f(3), 2 f(17,10));
+      x = x + h*f(t, x);
+   end;
+
+   /* Step size is 5 seconds */
+   h = 5;
+   put skip data (h);
+   put skip list ('  t    By formula', 'By Euler');
+   do t = 0 to 100 by 5;
+      put skip edit ( t, Tr + (T0 - Tr)/exp(k*t), y) (f(3), 2 f(17,10));
+      y = y + h*f(t, y);
+   end;
+
+   /* Step size is 10 seconds */
+   h = 10;
+   put skip data (h);
+   put skip list ('  t    By formula', 'By Euler');
+   do t = 0 to 100 by 10;
+      put skip edit (t, Tr + (T0 - Tr)/exp(k*t), z) (f(3), 2 f(17,10));
+      z = z + h*f(t, z);
+   end;
+
+f: procedure (dummy, T) returns (float);
+   declare dummy  fixed binary;
+   declare T float;
+
+   return ( -k*(T - Tr) );
+end f;
+
+end test;

Task/Euler-method/Perl-6/euler-method.pl6

@@ -0,0 +1,37 @@
+sub euler ( &f, $y0, $a, $b, $h ) {
+    my $y = $y0;
+    my @t_y;
+    for $a, * + $h ... * > $b -> $t {
+        @t_y[$t] = $y;
+        $y += $h * f( $t, $y );
+    }
+    return @t_y;
+}
+
+my $COOLING_RATE = 0.07;
+my $AMBIENT_TEMP =   20;
+my $INITIAL_TEMP =  100;
+my $INITIAL_TIME =    0;
+my $FINAL_TIME   =  100;
+
+sub f ( $time, $temp ) {
+    return -$COOLING_RATE * ( $temp - $AMBIENT_TEMP );
+}
+
+my @e;
+@e[$_] = euler( &f, $INITIAL_TEMP, $INITIAL_TIME, $FINAL_TIME, $_ ) for 2, 5, 10;
+
+say 'Time Analytic   Step2   Step5  Step10     Err2     Err5    Err10';
+
+for $INITIAL_TIME, * + 10 ... * >= $FINAL_TIME -> $t {
+
+    my $exact = $AMBIENT_TEMP + ($INITIAL_TEMP - $AMBIENT_TEMP)
+                              * (-$COOLING_RATE * $t).exp;
+
+    my $err = sub { @^a.map: { 100 * abs( $_ - $exact ) / $exact } }
+
+    my ( $a, $b, $c ) = map { @e[$_][$t] }, 2, 5, 10;
+
+    say $t.fmt('%4d '), ( $exact, $a, $b, $c )».fmt(' %7.3f'),
+                           $err.([$a, $b, $c])».fmt(' %7.3f%%');
+}

Task/Euler-method/PureBasic/euler-method.purebasic

@@ -0,0 +1,25 @@
+Define.d
+Prototype.d Func(Time, t)
+
+Procedure.d Euler(*F.Func, y0, a, b, h)
+  Protected y=y0, t=a
+  While t<=b
+    PrintN(RSet(StrF(t,3),7)+" "+RSet(StrF(y,3),7))
+    y + h * *F(t,y)
+    t + h
+  Wend
+EndProcedure
+
+Procedure.d newtonCoolingLaw(Time, t)
+  ProcedureReturn -0.07*(t-20)
+EndProcedure
+
+
+If OpenConsole()
+  Euler(@newtonCoolingLaw(), 100, 0, 100, 2)
+  Euler(@newtonCoolingLaw(), 100, 0, 100, 5)
+  Euler(@newtonCoolingLaw(), 100, 0, 100,10)
+
+  Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
+  CloseConsole()
+EndIf

Task/Euler-method/Run-BASIC/euler-method.run

@@ -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/XPL0/euler-method.xpl0

@@ -0,0 +1,38 @@
+include c:\cxpl\codes;  \intrinsic 'code' declarations
+
+proc Euler(Step);       \Display cooling temperatures using Euler's method
+int  Step;
+int  Time;  real Temp;
+[Text(0, "Step ");  IntOut(0, Step);  Text(0, " ");
+Time:= 0;  Temp:= 100.0;
+repeat  if rem(Time/10) = 0 then RlOut(0, Temp);
+        Temp:= Temp + float(Step) * (-0.07*(Temp-20.0));
+        Time:= Time + Step;
+until   Time > 100;
+CrLf(0);
+];
+
+real Time, Temp;
+[Format(6,0);                   \display time heading
+Text(0, "Time   ");
+Time:= 0.0;
+while Time <= 100.1 do          \(.1 avoids possible rounding error)
+        [RlOut(0, Time);
+        Time:= Time + 10.0;
+        ];
+CrLf(0);
+
+Format(3,2);                    \display cooling temps using differential eqn.
+Text(0, "Dif eq ");             \ dTemp(time)/dtime = -k*Temp
+Time:= 0.0;
+while Time <= 100.1 do
+        [Temp:= 20.0 + (100.0-20.0) * Exp(-0.07*Time);
+        RlOut(0, Temp);
+        Time:= Time + 10.0;
+        ];
+CrLf(0);
+
+Euler(2);                       \display cooling temps for various time steps
+Euler(5);
+Euler(10);
+]