Euler method: Difference between revisions
Add MATLAB implementation
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(Add MATLAB implementation) |
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Line 2,116:
euler[10, 100]
20.0005</pre>
=={{header|MATLAB}}==
{{trans|Julia}}
<syntaxhighlight lang="MATLAB}}">
clear all;close all;clc;
format longG;
% Main Script
for h = [5, 10]
fprintf('Step %d:\n\n', h);
tabular(15, 'Time', 'Euler', 'Analytic');
T0 = 100.0;
t0 = 0;
t1 = 100;
T = euler(@(T) -0.07 * (T - 20.0), T0, t0, t1, h);
for i = 1:length(T)
t = (i-1) * h;
analytic = 20.0 + 80.0 * exp(-0.07 * t);
tabular(15, t, round(T(i), 6), round(analytic, 6));
end
fprintf('\n');
end
function T = euler(f, T0, t0, t1, h)
% EULER A simple implementation of Euler's method for solving ODEs
% f - function handle for the derivative
% T0 - initial temperature
% t0, t1 - start and end times
% h - step size
T = T0;
for t = t0:h:t1
T(end+1) = T(end) + h * f(T(end));
end
end
function tabular(width, varargin)
% TABULAR Prints a series of values in a tabular form
% width - cell width
% varargin - variable number of arguments representing cells
for i = 1:length(varargin)
fprintf('%-*s', width, num2str(varargin{i}));
end
fprintf('\n');
end
</syntaxhighlight>
{{out}}
<pre>
Step 5:
Time Euler Analytic
0 100 100
5 72 76.375
10 53.8 59.7268
15 41.97 47.995
20 34.2805 39.7278
25 29.2823 33.9019
30 26.0335 29.7965
35 23.9218 26.9035
40 22.5492 24.8648
45 21.657 23.4282
50 21.077 22.4158
55 20.7001 21.7024
60 20.455 21.1996
65 20.2958 20.8454
70 20.1923 20.5957
75 20.125 20.4198
80 20.0812 20.2958
85 20.0528 20.2085
90 20.0343 20.1469
95 20.0223 20.1035
100 20.0145 20.073
105 20.0094 20.0514
Step 10:
Time Euler Analytic
0 100 100
10 44 59.7268
20 27.2 39.7278
30 22.16 29.7965
40 20.648 24.8648
50 20.1944 22.4158
60 20.0583 21.1996
70 20.0175 20.5957
80 20.0052 20.2958
90 20.0016 20.1469
100 20.0005 20.073
110 20.0001 20.0362
</pre>
=={{header|Maxima}}==
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