Euler method: Difference between revisions
→{{header|Pascal}}
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</pre>
=={{header|Ol}}==
{{trans|ObjectIcon}}
The output is meant to be fed into [[Gnuplot]]. You can run the program like this: <code>ol name-you-saved-the-program-as.scm | gnuplot</code>
(Gnuplot may substitute a different font.)
<syntaxhighlight lang="Scheme">
(define (euler-method f y0 a b h)
;; 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.
(let loop ((t a)
(y y0)
(point-pairs '()))
(let ((point-pairs (cons (cons t y) point-pairs)))
(if (<= b t)
(reverse point-pairs)
(loop (+ t h) (+ y (* h (f t y))) point-pairs)))))
(define (newton-cooling-step t Temperature)
;; Newton's cooling law, with temperature in Celsius:
;;
;; f(t, Temperature) = -0.07*(Temperature - 20)
;;
(* -0.07 (- Temperature 20)))
(define data-for-stepsize=2
(euler-method newton-cooling-step 100.0 0.0 100.0 2.0))
(define data-for-stepsize=5
(euler-method newton-cooling-step 100.0 0.0 100.0 5.0))
(define data-for-stepsize=10
(euler-method newton-cooling-step 100.0 0.0 100.0 10.0))
(define (display-point-pairs point-pairs)
(let loop ((p point-pairs))
(if (pair? p)
(begin
(display (inexact (caar p)))
(display " ")
(display (inexact (cdar p)))
(newline)
(loop (cdr p))))))
(display "set encoding utf8") (newline)
(display "set term png size 1000,750 font 'Farao Book,16'") (newline)
(display "set output 'newton-cooling-Scheme.png'") (newline)
(display "set grid") (newline)
(display "set title 'Newton’s Law of Cooling'") (newline)
(display "set xlabel 'Elapsed time (seconds)'") (newline)
(display "set ylabel 'Temperature (Celsius)'") (newline)
(display "set xrange [0:100]") (newline)
(display "set yrange [15:100]") (newline)
(display "y(x) = 20.0 + (80.0 * exp (-0.07 * x))") (newline)
(display "plot y(x) with lines title 'Analytic solution', \\") (newline)
(display " '-' with linespoints title 'Euler method, step size 2s', \\") (newline)
(display " '-' with linespoints title 'Step size 5s', \\") (newline)
(display " '-' with linespoints title 'Step size 10s'") (newline)
(display-point-pairs data-for-stepsize=2)
(display "e") (newline)
(display-point-pairs data-for-stepsize=5)
(display "e") (newline)
(display-point-pairs data-for-stepsize=10)
(display "e") (newline)
</syntaxhighlight>
{{out}}
[[File:Euler method Scheme--newton-cooling.2023.04.26.10.30.19.png|thumb|none|alt=A plot of the cooling data, for all the cases.]]
=={{header|Pascal}}==
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