Euler method: Difference between revisions

Euler method (view source)

Revision as of 22:05, 2 March 2019

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→‎version 2: changed a comment, changed or added whitespace, used a more idiomatic method for setting the numeric digits.

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rosettacode>Gerard Schildberger

Revision as of 21:52, 2 March 2019 (view source) rosettacode>Gerard Schildberger m (→‎version 2: used a template for the output section.) ← Older edit		Revision as of 22:05, 2 March 2019 (view source) rosettacode>Gerard Schildberger m (→‎version 2: changed a comment, changed or added whitespace, used a more idiomatic method for setting the numeric digits.) Newer edit →
Line 2,618: ===version 2=== This REXX version allows values to be specified via the command line (CL). <br>It also shows the percentage difference (analytic vs. Euler's method) for each calculation. <lang rexx>/REXX pgm solves example of Newton's cooling law via Euler's method (diff. step sizes)./ numeric digits length( e() - 1length(.) /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, @) $=Ti; inc= word(ss, Ssize) /the 1st value; obtain the increment./ do t=0 to Ti by inc /step through calculations by the inc./ a= format(Tr + (Ti-Tr)/exp(cct), 6,9) /calculate the analytic (exact) value./ say center(t,11) format($,6,3) 'ºC ' a "ºC" format(abs(a-$)/a100,6,2) '%' $=$ + inc cc * (Tr-$) /calc. next value via Euler's method. / end /t/ end /~~stepSize~~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</lang> {{out\|output\|text=  when using the default inputs:}} <pre>