Data update

Task/Euler-method/REXX/euler-method-2.rexx

@@ -1,25 +1,49 @@
-/*REXX pgm solves example of Newton's cooling law via Euler's method (diff. step sizes).*/
-e=2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138
-numeric digits length(e)   -  length(.)          /*use the number of decimal digits in E*/
-parse arg Ti Tr cc tt ss                         /*obtain optional arguments from the CL*/
-if Ti='' | Ti=","  then Ti= 100                  /*given?  Default:  initial temp in ºC.*/
-if Tr='' | Tr=","  then Tr=  20                  /*  "         "       room    "   "  " */
-if cc='' | cc=","  then cc=   0.07               /*  "         "     cooling constant.  */
-if tt='' | tt=","  then tt= 100                  /*  "         "    total time seconds. */
-if ss='' | ss=","  then ss=   2  5  10           /*  "         "      the step sizes.   */
-@= '═'                                           /*the character used in title separator*/
-     do sSize=1  for words(ss);    say;    say;    say center('time in'     , 11)
-     say center('seconds' , 11, @)                     center('Euler method', 16, @) ,
-         center('analytic', 18, @)                     center('difference'  , 14, @)
-     $=Ti;                  inc= word(ss, sSize) /*the 1st value;  obtain the increment.*/
-          do t=0  to Ti  by inc                  /*step through calculations by the inc.*/
-          a= format(Tr + (Ti-Tr)/exp(cc*t),6,10) /*calculate the analytic (exact) value.*/
-          say center(t,11)  format($,6,3)  'ºC '  a  "ºC"  format(abs(a-$)/a*100,6,2)  '%'
-          $= $   +   inc * cc * (Tr-$)           /*calc. next value via Euler's method. */
-          end   /*t*/
-     end        /*sSize*/
-exit                                             /*stick a fork in it,  we're all done. */
-/*──────────────────────────────────────────────────────────────────────────────────────*/
-exp: procedure expose e; arg x; ix= x%1; if abs(x-ix)>.5  then ix=ix+sign(x); x= x-ix; z=1
-     _=1;  w=1;    do j=1;  _= _*x/j;    z= (z+_)/1;      if z==w  then leave;         w=z
-                   end  /*j*/;           if z\==0  then z= e**ix * z;             return z
+-- 18 Sep 2025
+include Setting
+
+say "EULER METHOD FOR ODE y'=-0.07(y-20)"
+say version
+say
+call Task 0,100,2,100
+call Task 0,100,5,100
+call Task 0,100,10,100
+call Timer
+exit
+
+Task:
+-- Euler method
+procedure expose Memo.
+arg x0,xn,dx,y0
+say 'From' x0 'to' xn 'step' dx
+say '  x   Calc y      True y    Abs error Rel error'
+x=x0; y=y0
+do until x > xn
+   if x//10 = 0 then
+      call Show x,y
+   y+=dx*Dy(y); x+=dx
+end
+say
+return
+
+Show:
+-- Display a line
+procedure expose Memo.
+arg xx,yy
+yt=True(xx)
+say Format(xx,3,0) Format(yy,3,7) Format(yt,3,7),
+    Left(Std(Abs(yy-yt)),9) Left(Std(Abs(yy/yt-1)),9)
+return
+
+Dy:
+-- Differential equation
+procedure
+arg yy
+return -0.07*(yy-20)
+
+True:
+-- Real solution
+procedure expose Memo.
+arg xx
+return 20+(100-20)*Exp(-0.07*xx)
+
+include Math