Merge pull request #575 from algobytewise/Add-algorithm-Euler-method

Add algorithm Euler method

Maths/EulerMethod.js

@@ -0,0 +1,108 @@
+/*
+In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations. The method proceeds in a series of steps. At each step the y-value is calculated by evaluating the differential equation at the previous step, multiplying the result with the step-size and adding it to the last y-value: y_n+1 = y_n + stepSize * f(x_n, y_n).
+(description adapted from https://en.wikipedia.org/wiki/Euler_method )
+(see also: https://www.geeksforgeeks.org/euler-method-solving-differential-equation/ )
+*/
+
+/*
+Doctests
+> eulerStep(0, 0.1, 0, function(x, y){return x})
+0
+> eulerStep(2, 1, 1, function(x, y){return x * x})
+5
+> eulerFull(0, 3, 1, 0, function(x, y){return x})
+[{"x": 0, "y": 0}, {"x": 1, "y": 0}, {"x": 2, "y": 1}, {"x": 3, "y": 3}]
+> eulerFull(3, 4, 0.5, 1, function(x, y){return x * x})
+[{"x": 3, "y": 1}, {"x": 3.5, "y": 5.5}, {"x": 4, "y": 11.625}]
+*/
+
+function eulerStep (xCurrent, stepSize, yCurrent, differentialEquation) {
+  // calculates the next y-value based on the current value of x, y and the stepSize
+  const yNext = yCurrent + stepSize * differentialEquation(xCurrent, yCurrent)
+  return yNext
+}
+
+function eulerFull (xStart, xEnd, stepSize, yStart, differentialEquation) {
+  // loops through all the steps until xEnd is reached, adds a point for each step and then returns all the points
+  const points = [{ x: xStart, y: yStart }]
+  let yCurrent = yStart
+  let xCurrent = xStart
+
+  while (xCurrent < xEnd) {
+    // Euler method for next step
+    yCurrent = eulerStep(xCurrent, stepSize, yCurrent, differentialEquation)
+    xCurrent += stepSize
+    points.push({ x: xCurrent, y: yCurrent })
+  }
+
+  return points
+}
+
+function plotLine (label, points, width, height) {
+  // utility function to plot the results
+
+  // container needed to control the size of the canvas
+  const container = document.createElement('div')
+  container.style.width = width + 'px'
+  container.style.height = height + 'px'
+  document.body.append(container)
+
+  // the canvas for plotting
+  const canvas = document.createElement('canvas')
+  container.append(canvas)
+
+  // Chart-class from chartjs
+  const chart = new Chart(canvas, { // eslint-disable-line
+    type: 'scatter',
+    data: {
+      datasets: [{
+        label: label,
+        data: points,
+        showLine: true,
+        fill: false,
+        tension: 0,
+        borderColor: 'black'
+      }]
+    },
+    options: {
+      maintainAspectRatio: false,
+      responsive: true
+    }
+  })
+}
+
+function exampleEquation1 (x, y) {
+  return x
+}
+
+// example from https://en.wikipedia.org/wiki/Euler_method
+function exampleEquation2 (x, y) {
+  return y
+}
+
+// example from https://www.geeksforgeeks.org/euler-method-solving-differential-equation/
+function exampleEquation3 (x, y) {
+  return x + y + x * y
+}
+
+const points1 = eulerFull(0, 4, 0.1, 0, exampleEquation1)
+const points2 = eulerFull(0, 4, 0.1, 1, exampleEquation2)
+const points3 = eulerFull(0, 0.1, 0.025, 1, exampleEquation3)
+
+console.log(points1)
+console.log(points2)
+console.log(points3)
+
+// plot the results if the script is executed in a browser with a window-object
+if (typeof window !== 'undefined') {
+  const script = document.createElement('script')
+
+  // using chartjs
+  script.src = 'https://www.chartjs.org/dist/2.9.4/Chart.min.js'
+  script.onload = function () {
+    plotLine('example 1: dy/dx = x', points1, 600, 400)
+    plotLine('example 2: dy/dx = y', points2, 600, 400)
+    plotLine('example 3: dy/dx = x + y + x * y', points3, 600, 400)
+  }
+  document.body.append(script)
+}