Data update

Task/Euler-method/Dart/euler-method.dart

@@ -0,0 +1,44 @@
+import 'dart:math';
+import "dart:io";
+
+const double k = 0.07;
+const double initialTemp = 100.0;
+const double finalTemp = 20.0;
+const int startTime = 0;
+const int endTime = 100;
+
+void ivpEuler(double Function(double, double) function, double initialValue, int step) {
+  stdout.write(' Step ${step.toString().padLeft(2)}: ');
+  var y = initialValue;
+  for (int t = startTime; t <= endTime; t += step) {
+    if (t % 10 == 0) {
+      stdout.write(y.toStringAsFixed(3).padLeft(7));
+    }
+    y += step * function(t.toDouble(), y);
+  }
+  print('');
+}
+
+void analytic() {
+  stdout.write('    Time: ');
+  for (int t = startTime; t <= endTime; t += 10) {
+    stdout.write(t.toString().padLeft(7));
+  }
+  stdout.write('\nAnalytic: ');
+  for (int t = startTime; t <= endTime; t += 10) {
+    var temp = finalTemp + (initialTemp - finalTemp) * exp(-k * t);
+    stdout.write(temp.toStringAsFixed(3).padLeft(7));
+  }
+  print('');
+}
+
+double cooling(double t, double temp) {
+  return -k * (temp - finalTemp);
+}
+
+void main() {
+  analytic();
+  ivpEuler(cooling, initialTemp, 2);
+  ivpEuler(cooling, initialTemp, 5);
+  ivpEuler(cooling, initialTemp, 10);
+}

Task/Euler-method/MATLAB/euler-method.m

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+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

Task/Euler-method/Uiua/euler-method.uiua

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+"Euler Solution"
+T ← 100 # initial starting temp
+TR ← 20 # room temp
+TMINUSTR ← - TR T
+h ← 10      # step size
+k ← 0.07    # coefficent
+TEND ← 100  # end time
+n ← ÷ h 100 # steps
+# inital starting point
+T
+.
+# ..  clone the top of stack and take if for next step
+# repeat the steps n times with ⍥
+Solution ← [⍥(.. - × h × k - TR)]+ n 1
+⇌ ⊂ Solution T
+
+# analytical solution
+"Analytical Solution"
+# apply function to LIST
+List ← × k × h ⇡n
+# Analytical solution applied
++ TR × TMINUSTR ⁿ ¯List e