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September Morn Update

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Ingy döt Net 2019-09-12 10:33:56 -07:00
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Task/Euler-method/REXX/euler-method-2.rexx
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@ -1,26 +1,25 @@
/*REXX pgm solves example of Newton's cooling law via Euler's method (diff. step sizes).*/
numeric digits length( e() - 1) /*use the number of decimal digits in E*/
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. */
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, @)
$=Ti; inc=word(ss,Ssize) /*the 1st value; obtain the increment.*/
do t=0 to Ti by inc /*step through calculations by the inc.*/
a=format(Tr + (Ti-Tr)/exp(cc*t),6,9) /*calculate the analytic (exact) value.*/
say center(t,11) format($,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 /*stepSize*/
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. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
e: return 2.718281828459045235360287471352662497757247093699959574966967627724076630353548
/*──────────────────────────────────────────────────────────────────────────────────────*/
exp: procedure; parse 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
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