Euler method: Difference between revisions
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m (→version 2: used a template for the output section.) |
m (→version 2: changed a comment, changed or added whitespace, used a more idiomatic method for setting the numeric digits.) |
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===version 2=== |
===version 2=== |
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This REXX version allows values to be specified via the command line (CL). |
This REXX version allows values to be specified via the command line (CL). |
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<br>It also shows the percentage difference (analytic vs. Euler's method) for each calculation. |
<br>It also shows the percentage difference (analytic vs. Euler's method) for each calculation. |
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<lang rexx>/*REXX pgm solves example of Newton's cooling law via Euler's method (diff. step sizes).*/ |
<lang rexx>/*REXX pgm solves example of Newton's cooling law via Euler's method (diff. step sizes).*/ |
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numeric digits length( e() - |
numeric digits length( e() - length(.) /*use the number of decimal digits in E*/ |
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parse arg Ti Tr cc tt ss /*obtain optional arguments from the CL*/ |
parse arg Ti Tr cc tt ss /*obtain optional arguments from the CL*/ |
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if Ti |
if Ti='' | Ti="," then Ti= 100 /*given? Default: initial temp in ºC.*/ |
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if Tr |
if Tr='' | Tr="," then Tr= 20 /* " " room " " " */ |
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if cc |
if cc='' | cc="," then cc= 0.07 /* " " cooling constant. */ |
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if tt |
if tt='' | tt="," then tt= 100 /* " " total time seconds. */ |
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if ss |
if ss='' | ss="," then ss= 2 5 10 /* " " the step sizes. */ |
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@= '═' /*the character used in title separator*/ |
@= '═' /*the character used in title separator*/ |
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do sSize=1 for words(ss); say; say; say center('time in' , 11) |
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say center('seconds' , 11, @) center('Euler method', 16, @) , |
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center('analytic', 18, @) center('difference' , 14, @) |
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$=Ti; inc= word(ss, Ssize) /*the 1st value; obtain the increment.*/ |
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do t=0 to Ti by inc /*step through calculations by the inc.*/ |
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a= format(Tr + (Ti-Tr)/exp(cc*t), 6,9) /*calculate the analytic (exact) value.*/ |
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say center(t,11) format($,6,3) 'ºC ' a "ºC" format(abs(a-$)/a*100,6,2) '%' |
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$=$ + inc * cc * (Tr-$) /*calc. next value via Euler's method. */ |
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end /*t*/ |
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end /*sSize*/ |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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e: return 2.718281828459045235360287471352662497757247093699959574966967627724076630353548 |
e: return 2.718281828459045235360287471352662497757247093699959574966967627724076630353548 |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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exp: procedure; parse arg x; |
exp: procedure; parse arg x; ix= x%1; if abs(x-ix)>.5 then ix= ix+sign(x); x=x-ix; z=1 |
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_=1; w=1; do j=1; _=_*x/j; |
_=1; w=1; do j=1; _= _*x/j; z= (z+_)/1; if z==w then leave; w=z; end /*j*/ |
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if z\==0 then z=e()**ix * z; |
if z\==0 then z= e()**ix * z; return z</lang> |
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{{out|output|text= when using the default inputs:}} |
{{out|output|text= when using the default inputs:}} |
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<pre> |
<pre> |
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