59 lines
2.1 KiB
Text
59 lines
2.1 KiB
Text
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(define (euler-method f y0 a b h)
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;; Approximate y(t) in dy/dt=f(t,y), y(a)=y0, t going from a to b
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;; with positive step size h. Produce a list of point pairs as
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;; output.
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(let loop ((t a)
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(y y0)
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(point-pairs '()))
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(let ((point-pairs (cons (cons t y) point-pairs)))
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(if (<= b t)
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(reverse point-pairs)
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(loop (+ t h) (+ y (* h (f t y))) point-pairs)))))
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(define (newton-cooling-step t Temperature)
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;; Newton's cooling law, with temperature in Celsius:
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;;
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;; f(t, Temperature) = -0.07*(Temperature - 20)
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;;
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(* -0.07 (- Temperature 20)))
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(define data-for-stepsize=2
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(euler-method newton-cooling-step 100.0 0.0 100.0 2.0))
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(define data-for-stepsize=5
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(euler-method newton-cooling-step 100.0 0.0 100.0 5.0))
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(define data-for-stepsize=10
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(euler-method newton-cooling-step 100.0 0.0 100.0 10.0))
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(define (display-point-pairs point-pairs)
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(let loop ((p point-pairs))
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(if (pair? p)
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(begin
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(display (inexact (caar p)))
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(display " ")
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(display (inexact (cdar p)))
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(newline)
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(loop (cdr p))))))
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(display "set encoding utf8") (newline)
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(display "set term png size 1000,750 font 'Farao Book,16'") (newline)
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(display "set output 'newton-cooling-Scheme.png'") (newline)
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(display "set grid") (newline)
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(display "set title 'Newton’s Law of Cooling'") (newline)
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(display "set xlabel 'Elapsed time (seconds)'") (newline)
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(display "set ylabel 'Temperature (Celsius)'") (newline)
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(display "set xrange [0:100]") (newline)
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(display "set yrange [15:100]") (newline)
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(display "y(x) = 20.0 + (80.0 * exp (-0.07 * x))") (newline)
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(display "plot y(x) with lines title 'Analytic solution', \\") (newline)
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(display " '-' with linespoints title 'Euler method, step size 2s', \\") (newline)
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(display " '-' with linespoints title 'Step size 5s', \\") (newline)
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(display " '-' with linespoints title 'Step size 10s'") (newline)
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(display-point-pairs data-for-stepsize=2)
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(display "e") (newline)
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(display-point-pairs data-for-stepsize=5)
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(display "e") (newline)
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(display-point-pairs data-for-stepsize=10)
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(display "e") (newline)
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