Euler method: Difference between revisions
→{{header|Swift}}
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</pre>
=={{header|Standard ML}}==
{{trans|Ol}}
{{works with|Poly/ML|5.9}}
{{works with|MLton|20210117}}
This program outputs commands for [[Gnuplot]], which will produce a PNG. Run the program with a command such as <code>poly --script name_you_gave_the_file.sml | gnuplot</code>.
<syntaxhighlight lang="sml">
(* Approximate y(t) in dy/dt=f(t,y), y(a)=y0, t going from a to b with
positive step size h. Produce a list of point pairs as output. *)
fun eulerMethod (f, y0, a, b, h) =
let
fun loop (t, y, pointPairs) =
let
val pointPairs = (t, y) :: pointPairs
in
if b <= t then
rev pointPairs
else
loop (t + h, y + (h * f (t, y)), pointPairs)
end
in
loop (a, y0, nil)
end
(* How to step temperature according to Newton's law of cooling. *)
fun f (t, temp) = ~0.07 * (temp - 20.0)
val data2 = eulerMethod (f, 100.0, 0.0, 100.0, 2.0)
and data5 = eulerMethod (f, 100.0, 0.0, 100.0, 5.0)
and data10 = eulerMethod (f, 100.0, 0.0, 100.0, 10.0)
fun printPointPairs pointPairs =
app (fn (t, y) => (print (Real.toString t);
print " ";
print (Real.toString y);
print "\n"))
pointPairs
;
print ("set encoding utf8\n");
print ("set term png size 1000,750 font 'Brioso Pro,16'\n");
print ("set output 'newton-cooling-SML.png'\n");
print ("set grid\n");
print ("set title 'Newton\\U+2019s Law of Cooling'\n");
print ("set xlabel 'Elapsed time (seconds)'\n");
print ("set ylabel 'Temperature (Celsius)'\n");
print ("set xrange [0:100]\n");
print ("set yrange [15:100]\n");
print ("y(x) = 20.0 + (80.0 * exp (-0.07 * x))\n");
print ("plot y(x) with lines title 'Analytic solution', \\\n");
print (" '-' with linespoints title 'Euler method, step size 2s', \\\n");
print (" '-' with linespoints title 'Step size 5s', \\\n");
print (" '-' with linespoints title 'Step size 10s'\n");
printPointPairs data2;
print ("e\n");
printPointPairs data5;
print ("e\n");
printPointPairs data10;
print ("e\n");
</syntaxhighlight>
{{out}}
[[File:Euler method SML--newton-cooling.2023.04.26.14.07.02.png|thumb|none|alt=The output of the Standard ML program, as plotted by Gnuplot.]]
=={{header|Swift}}==
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