Data update

Task/Runge-Kutta-method/Ada/runge-kutta-method.ada

@@ -1,52 +0,0 @@
-with Ada.Text_IO; use Ada.Text_IO;
-with Ada.Numerics.Generic_Elementary_Functions;
-procedure RungeKutta is
-   type Floaty is digits 15;
-   type Floaty_Array is array (Natural range <>) of Floaty;
-   package FIO is new Ada.Text_IO.Float_IO(Floaty); use FIO;
-   type Derivative is access function(t, y : Floaty) return Floaty;
-   package Math is new Ada.Numerics.Generic_Elementary_Functions (Floaty);
-   function calc_err (t, calc : Floaty) return Floaty;
-
-   procedure Runge (yp_func : Derivative; t, y : in out Floaty_Array;
-                    dt : Floaty) is
-      dy1, dy2, dy3, dy4 : Floaty;
-   begin
-      for n in t'First .. t'Last-1 loop
-         dy1 := dt * yp_func(t(n), y(n));
-         dy2 := dt * yp_func(t(n) + dt / 2.0, y(n) + dy1 / 2.0);
-         dy3 := dt * yp_func(t(n) + dt / 2.0, y(n) + dy2 / 2.0);
-         dy4 := dt * yp_func(t(n) + dt, y(n) + dy3);
-         t(n+1) := t(n) + dt;
-         y(n+1) := y(n) + (dy1 + 2.0 * (dy2 + dy3) + dy4) / 6.0;
-      end loop;
-   end Runge;
-
-   procedure Print (t, y : Floaty_Array; modnum : Positive) is begin
-      for i in t'Range loop
-         if i mod modnum = 0 then
-            Put("y(");   Put (t(i), Exp=>0, Fore=>0, Aft=>1);
-            Put(") = "); Put (y(i), Exp=>0, Fore=>0, Aft=>8);
-            Put(" Error:"); Put (calc_err(t(i),y(i)), Aft=>5);
-            New_Line;
-         end if;
-      end loop;
-   end Print;
-
-   function yprime (t, y : Floaty) return Floaty is begin
-      return t * Math.Sqrt (y);
-   end yprime;
-   function calc_err (t, calc : Floaty) return Floaty is
-      actual : constant Floaty := (t**2 + 4.0)**2 / 16.0;
-   begin return abs(actual-calc);
-   end calc_err;
-
-   dt : constant Floaty := 0.10;
-   N : constant Positive := 100;
-   t_arr, y_arr : Floaty_Array(0 .. N);
-begin
-   t_arr(0) := 0.0;
-   y_arr(0) := 1.0;
-   Runge (yprime'Access, t_arr, y_arr, dt);
-   Print (t_arr, y_arr, 10);
-end RungeKutta;

Task/Runge-Kutta-method/PowerShell/runge-kutta-method.psh

@@ -1,36 +0,0 @@
-function Runge-Kutta (${function:F}, ${function:y}, $y0, $t0, $dt, $tEnd) {
-    function RK ($tn,$yn)  {
-        $y1 = $dt*(F -t $tn -y $yn)
-        $y2 = $dt*(F -t ($tn + (1/2)*$dt) -y ($yn + (1/2)*$y1))
-        $y3 = $dt*(F -t ($tn + (1/2)*$dt) -y ($yn + (1/2)*$y2))
-        $y4 = $dt*(F -t ($tn + $dt) -y ($yn + $y3))
-        $yn + (1/6)*($y1 + 2*$y2 + 2*$y3 + $y4)
-    }
-    function time ($t0, $dt, $tEnd)  {
-        $end = [MATH]::Floor(($tEnd - $t0)/$dt)
-        foreach ($_ in 0..$end) { $_*$dt + $t0 }
-    }
-    $time, $yn, $t = (time $t0 $dt $tEnd), $y0, 0
-    foreach ($tn in $time) {
-        if($t -eq $tn) {
-            [pscustomobject]@{
-                t = "$tn"
-                y = "$yn"
-                error = "$([MATH]::abs($yn - (y $tn)))"
-            }
-            $t += 1
-        }
-        $yn = RK $tn $yn
-    }
-}
-function F ($t,$y)  {
-    $t * [MATH]::Sqrt($y)
-}
-function y ($t)  {
-    (1/16) * [MATH]::Pow($t*$t + 4,2)
-}
-$y0 = 1
-$t0 = 0
-$dt = 0.1
-$tEnd = 10
-Runge-Kutta  F y $y0 $t0  $dt  $tEnd

Task/Runge-Kutta-method/REXX/runge-kutta-method.rexx

@@ -1,51 +1,51 @@
--- 28 Jul 2025
-include Settings
+-- 18 Sep 2025
+include Setting
+numeric digits 16
 
-say "RUNGE-KUTTA METHOD FOR ODE y'=x*SqRt(y)"
+say "RUNGE-KUTTA METHOD FOR ODE y'=x*Sqrt(y)"
 say version
 say
-numeric digits 9
 call Task 0,10,1/10,1
-numeric digits 16
-call Task 0,10,1/10,1
-numeric digits 9
-call Task 0,10,1/20,1
-numeric digits 16
-call Task 0,10,1/20,1
-call Timer
 exit
 
 Task:
+-- Runge-Kutta method
 procedure expose Memo.
 arg x0,xn,dx,y0
+say 'From' x0 'to' xn 'step' dx
+say ' x   Calc y      True y    Abs err    Rel err'
 x=x0; y=y0
-say 'From' x0 'to' xn 'step' dx 'with' Digits() 'digits'
-say ' x       Calc y       True y  Abs error  Rel error'
-call Show x,y
-do until x >= xn
-   dy1=dx*DyDx(x,y)
-   dy2=dx*DyDx(x+dx/2,y+dy1/2)
-   dy3=dx*DyDx(x+dx/2,y+dy2/2)
-   dy4=dx*DyDx(x+dx,y+dy3)
-   x=x+dx; y=y+(dy1+2*dy2+2*dy3+dy4)/6
+do until x > xn
    if Integer(x) then
       call Show x,y
+   dy1=dx*Dy(x,y)
+   dy2=dx*Dy(x+dx/2,y+dy1/2)
+   dy3=dx*Dy(x+dx/2,y+dy2/2)
+   dy4=dx*Dy(x+dx,y+dy3)
+   x+=dx; y+=(dy1+2*dy2+2*dy3+dy4)/6
 end
 say
 return
 
-DyDx:
+Show:
+-- Display a line
+procedure
+arg xx,yy
+yt=True(xx)
+say Format(xx,2,0) Format(yy,3,7) Format(True(xx),3,7),
+    Left(Std(Abs(yy-True(xx))),10) Left(Std(Abs(yy/True(xx)-1)),10)
+return
+
+Dy:
+-- Differential equation
+procedure expose Memo.
 arg xx,yy
 return xx*SqRt(yy)
 
 True:
+-- Real solution
+procedure
 arg xx
 return (xx**2+4)**2/16
 
-Show:
-arg xx,yy
-say Format(xx,2,0) Format(yy,3,8) Format(True(xx),3,8),
-    Left(Std(Abs(yy-True(xx))),10) Left(Std(Abs(yy/True(xx)-1)),10)
-return
-
 include Math