Data update

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