Euler method: Difference between revisions

Content added Content deleted
m (→‎version 2: added a missed cut n' paste output line.)
m (→‎version 2: updated the output.)
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$=Ti; inc= word(ss, sSize) /*the 1st value; obtain the increment.*/
$=Ti; inc= word(ss, sSize) /*the 1st value; obtain the increment.*/
do t=0 to Ti by inc /*step through calculations by the inc.*/
do t=0 to Ti by inc /*step through calculations by the inc.*/
a= format(Tr + (Ti-Tr)/exp(cc*t), 6,9) /*calculate the analytic (exact) value.*/
a= format(Tr + (Ti-Tr)/exp(cc*t),6,10) /*calculate the analytic (exact) value.*/
say center(t,11) format($,6,3) 'ºC ' a "ºC" format(abs(a-$)/a*100,6,2) '%'
say center(t,11) format($,6,3) 'ºC ' a "ºC" format(abs(a-$)/a*100,6,2) '%'
$= $ + inc * cc * (Tr-$) /*calc. next value via Euler's method. */
$= $ + inc * cc * (Tr-$) /*calc. next value via Euler's method. */
Line 2,712: Line 2,712:
time in
time in
══seconds══ ══Euler method══ ═════analytic═════ ══difference══
══seconds══ ══Euler method══ ═════analytic═════ ══difference══
0 100.000 ºC 100.000000000 ºC 0.00 %
0 100.000 ºC 100.0000000000 ºC 0.00 %
2 88.800 ºC 89.548658832 ºC 0.84 %
2 88.800 ºC 89.5486588319 ºC 0.84 %
4 79.168 ºC 80.462699316 ºC 1.61 %
4 79.168 ºC 80.4626993165 ºC 1.61 %
6 70.884 ºC 72.563745585 ºC 2.31 %
6 70.884 ºC 72.5637455852 ºC 2.31 %
8 63.761 ºC 65.696725108 ºC 2.95 %
8 63.761 ºC 65.6967251079 ºC 2.95 %
10 57.634 ºC 59.726824303 ºC 3.50 %
10 57.634 ºC 59.7268243033 ºC 3.50 %
12 52.365 ºC 54.536841874 ºC 3.98 %
12 52.365 ºC 54.5368418743 ºC 3.98 %
14 47.834 ºC 50.024887908 ºC 4.38 %
14 47.834 ºC 50.0248879081 ºC 4.38 %
16 43.937 ºC 46.102383570 ºC 4.70 %
16 43.937 ºC 46.1023835698 ºC 4.70 %
18 40.586 ºC 42.692322120 ºC 4.93 %
18 40.586 ºC 42.6923221200 ºC 4.93 %
20 37.704 ºC 39.727757115 ºC 5.09 %
20 37.704 ºC 39.7277571153 ºC 5.09 %
22 35.226 ºC 37.150488114 ºC 5.18 %
22 35.226 ºC 37.1504881142 ºC 5.18 %
24 33.094 ºC 34.909918083 ºC 5.20 %
24 33.094 ºC 34.9099180832 ºC 5.20 %
26 31.261 ºC 32.962060075 ºC 5.16 %
26 31.261 ºC 32.9620600747 ºC 5.16 %
28 29.684 ºC 31.268673674 ºC 5.07 %
28 29.684 ºC 31.2686736737 ºC 5.07 %
30 28.328 ºC 29.796514260 ºC 4.93 %
30 28.328 ºC 29.7965142602 ºC 4.93 %
32 27.163 ºC 28.516680350 ºC 4.75 %
32 27.163 ºC 28.5166803503 ºC 4.75 %
34 26.160 ºC 27.404046201 ºC 4.54 %
34 26.160 ºC 27.4040462008 ºC 4.54 %
36 25.297 ºC 26.436768540 ºC 4.31 %
36 25.297 ºC 26.4367685400 ºC 4.31 %
38 24.556 ºC 25.595857740 ºC 4.06 %
38 24.556 ºC 25.5958577396 ºC 4.06 %
40 23.918 ºC 24.864805010 ºC 3.81 %
40 23.918 ºC 24.8648050100 ºC 3.81 %
42 23.369 ºC 24.229258299 ºC 3.55 %
42 23.369 ºC 24.2292582991 ºC 3.55 %
44 22.898 ºC 23.676740532 ºC 3.29 %
44 22.898 ºC 23.6767405319 ºC 3.29 %
46 22.492 ºC 23.196404661 ºC 3.04 %
46 22.492 ºC 23.1964046609 ºC 3.04 %
48 22.143 ºC 22.778820716 ºC 2.79 %
48 22.143 ºC 22.7788207156 ºC 2.79 %
50 21.843 ºC 22.415790674 ºC 2.55 %
50 21.843 ºC 22.4157906738 ºC 2.55 %
52 21.585 ºC 22.100187517 ºC 2.33 %
52 21.585 ºC 22.1001875173 ºC 2.33 %
54 21.363 ºC 21.825815314 ºC 2.12 %
54 21.363 ºC 21.8258153140 ºC 2.12 %
56 21.172 ºC 21.587287580 ºC 1.92 %
56 21.172 ºC 21.5872875795 ºC 1.92 %
58 21.008 ºC 21.379921529 ºC 1.74 %
58 21.008 ºC 21.3799215292 ºC 1.74 %
60 20.867 ºC 21.199646146 ºC 1.57 %
60 20.867 ºC 21.1996461456 ºC 1.57 %
62 20.746 ºC 21.042922256 ºC 1.41 %
62 20.746 ºC 21.0429222563 ºC 1.41 %
64 20.641 ºC 20.906673052 ºC 1.27 %
64 20.641 ºC 20.9066730524 ºC 1.27 %
66 20.551 ºC 20.788223685 ºC 1.14 %
66 20.551 ºC 20.7882236849 ºC 1.14 %
68 20.474 ºC 20.685248752 ºC 1.02 %
68 20.474 ºC 20.6852487518 ºC 1.02 %
70 20.408 ºC 20.595726646 ºC 0.91 %
70 20.408 ºC 20.5957266457 ºC 0.91 %
72 20.351 ºC 20.517899865 ºC 0.81 %
72 20.351 ºC 20.5178998655 ºC 0.81 %
74 20.302 ºC 20.450240513 ºC 0.73 %
74 20.302 ºC 20.4502405132 ºC 0.73 %
76 20.259 ºC 20.391420298 ºC 0.65 %
76 20.259 ºC 20.3914202980 ºC 0.65 %
78 20.223 ºC 20.340284460 ºC 0.58 %
78 20.223 ºC 20.3402844596 ºC 0.58 %
80 20.192 ºC 20.295829097 ºC 0.51 %
80 20.192 ºC 20.2958290973 ºC 0.51 %
82 20.165 ºC 20.257181462 ºC 0.45 %
82 20.165 ºC 20.2571814620 ºC 0.45 %
84 20.142 ºC 20.223582822 ºC 0.40 %
84 20.142 ºC 20.2235828220 ºC 0.40 %
86 20.122 ºC 20.194373568 ºC 0.36 %
86 20.122 ºC 20.1943735676 ºC 0.36 %
88 20.105 ºC 20.168980262 ºC 0.32 %
88 20.105 ºC 20.1689802617 ºC 0.32 %
90 20.090 ºC 20.146904382 ºC 0.28 %
90 20.090 ºC 20.1469043822 ºC 0.28 %
92 20.078 ºC 20.127712534 ºC 0.25 %
92 20.078 ºC 20.1277125344 ºC 0.25 %
94 20.067 ºC 20.111027944 ºC 0.22 %
94 20.067 ºC 20.1110279436 ºC 0.22 %
96 20.057 ºC 20.096523057 ºC 0.19 %
96 20.057 ºC 20.0965230571 ºC 0.19 %
98 20.049 ºC 20.083913115 ºC 0.17 %
98 20.049 ºC 20.0839131146 ºC 0.17 %
100 20.042 ºC 20.072950557 ºC 0.15 %
100 20.042 ºC 20.0729505572 ºC 0.15 %




time in
time in
══seconds══ ══Euler method══ ═════analytic═════ ══difference══
══seconds══ ══Euler method══ ═════analytic═════ ══difference══
0 100.000 ºC 100.000000000 ºC 0.00 %
0 100.000 ºC 100.0000000000 ºC 0.00 %
5 72.000 ºC 76.375047177 ºC 5.73 %
5 72.000 ºC 76.3750471775 ºC 5.73 %
10 53.800 ºC 59.726824303 ºC 9.92 %
10 53.800 ºC 59.7268243033 ºC 9.92 %
15 41.970 ºC 47.995019929 ºC 12.55 %
15 41.970 ºC 47.9950199289 ºC 12.55 %
20 34.281 ºC 39.727757115 ºC 13.71 %
20 34.281 ºC 39.7277571153 ºC 13.71 %
25 29.282 ºC 33.901915476 ºC 13.63 %
25 29.282 ºC 33.9019154760 ºC 13.63 %
30 26.034 ºC 29.796514260 ºC 12.63 %
30 26.034 ºC 29.7965142602 ºC 12.63 %
35 23.922 ºC 26.903486920 ºC 11.08 %
35 23.922 ºC 26.9034869199 ºC 11.08 %
40 22.549 ºC 24.864805010 ºC 9.31 %
40 22.549 ºC 24.8648050100 ºC 9.31 %
45 21.657 ºC 23.428170149 ºC 7.56 %
45 21.657 ºC 23.4281701494 ºC 7.56 %
50 21.077 ºC 22.415790674 ºC 5.97 %
50 21.077 ºC 22.4157906738 ºC 5.97 %
55 20.700 ºC 21.702378915 ºC 4.62 %
55 20.700 ºC 21.7023789151 ºC 4.62 %
60 20.455 ºC 21.199646146 ºC 3.51 %
60 20.455 ºC 21.1996461456 ºC 3.51 %
65 20.296 ºC 20.845376351 ºC 2.64 %
65 20.296 ºC 20.8453763507 ºC 2.64 %
70 20.192 ºC 20.595726646 ºC 1.96 %
70 20.192 ºC 20.5957266457 ºC 1.96 %
75 20.125 ºC 20.419801472 ºC 1.44 %
75 20.125 ºC 20.4198014719 ºC 1.44 %
80 20.081 ºC 20.295829097 ºC 1.06 %
80 20.081 ºC 20.2958290973 ºC 1.06 %
85 20.053 ºC 20.208467241 ºC 0.77 %
85 20.053 ºC 20.2084672415 ºC 0.77 %
90 20.034 ºC 20.146904382 ºC 0.56 %
90 20.034 ºC 20.1469043822 ºC 0.56 %
95 20.022 ºC 20.103521768 ºC 0.40 %
95 20.022 ºC 20.1035217684 ºC 0.40 %
100 20.014 ºC 20.072950557 ºC 0.29 %
100 20.014 ºC 20.0729505572 ºC 0.29 %




time in
time in
══seconds══ ══Euler method══ ═════analytic═════ ══difference══
══seconds══ ══Euler method══ ═════analytic═════ ══difference══
0 100.000 ºC 100.000000000 ºC 0.00 %
0 100.000 ºC 100.0000000000 ºC 0.00 %
10 44.000 ºC 59.726824303 ºC 26.33 %
10 44.000 ºC 59.7268243033 ºC 26.33 %
20 27.200 ºC 39.727757115 ºC 31.53 %
20 27.200 ºC 39.7277571153 ºC 31.53 %
30 22.160 ºC 29.796514260 ºC 25.63 %
30 22.160 ºC 29.7965142602 ºC 25.63 %
40 20.648 ºC 24.864805010 ºC 16.96 %
40 20.648 ºC 24.8648050100 ºC 16.96 %
50 20.194 ºC 22.415790674 ºC 9.91 %
50 20.194 ºC 22.4157906738 ºC 9.91 %
60 20.058 ºC 21.199646146 ºC 5.38 %
60 20.058 ºC 21.1996461456 ºC 5.38 %
70 20.017 ºC 20.595726646 ºC 2.81 %
70 20.017 ºC 20.5957266457 ºC 2.81 %
80 20.005 ºC 20.295829097 ºC 1.43 %
80 20.005 ºC 20.2958290973 ºC 1.43 %
90 20.002 ºC 20.146904382 ºC 0.72 %
90 20.002 ºC 20.1469043822 ºC 0.72 %
100 20.000 ºC 20.072950557 ºC 0.36 %
100 20.000 ºC 20.0729505572 ºC 0.36 %
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