From 0533b7df32fe22feea2344e5f616d5867babba68 Mon Sep 17 00:00:00 2001
From: Kees van Kempen <k.vankempen@student.science.ru.nl>
Date: Tue, 8 Mar 2022 16:03:55 +0100
Subject: [PATCH] 09: Add Koen's functions for task 3

---
 .../9 Ordinary Differential Equations.ipynb   | 21 ++++++++++++-------
 1 file changed, 14 insertions(+), 7 deletions(-)

diff --git a/Week 5/9 Ordinary Differential Equations.ipynb b/Week 5/9 Ordinary Differential Equations.ipynb
index d2abc78..242a58b 100644
--- a/Week 5/9 Ordinary Differential Equations.ipynb	
+++ b/Week 5/9 Ordinary Differential Equations.ipynb	
@@ -388,7 +388,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -406,16 +406,23 @@
    "outputs": [],
    "source": [
     "def phi_euler_modified(x, y, f, i):\n",
-    "    # YOUR CODE HERE\n",
-    "    raise NotImplementedError()\n",
+    "    h = x[i]-x[i-1]\n",
+    "    phi = f(x[i-1]+0.5*h, y[i-1]+0.5*h*f(x[i-1],y[i-1]))\n",
+    "    return phi\n",
     "    \n",
     "def phi_heun(x, y, f, i):\n",
-    "    # YOUR CODE HERE\n",
-    "    raise NotImplementedError()\n",
+    "    h = x[i]-x[i-1]\n",
+    "    phi = 0.5*(f(x[i-1],y[i-1])+f(x[i-1]+h,y[i-1]+h*f(x[i-1],y[i-1])))\n",
+    "    return phi\n",
     "    \n",
     "def phi_rk4(x, y, f, i):\n",
-    "    # YOUR CODE HERE\n",
-    "    raise NotImplementedError()"
+    "    h = x[i]-x[i-1]\n",
+    "    k1 = f(x[i-1],y[i-1])\n",
+    "    k2 = f(x[i-1]+0.5*h,y[i-1]+0.5*h*k1)\n",
+    "    k3 = f(x[i-1]+0.5*h,y[i-1]+0.5*h*k2)\n",
+    "    k4 = f(x[i-1]+h,y[i-1]+h*k3)\n",
+    "    phi = (1/6)*(k1+2*k2+2*k3+k4)\n",
+    "    return phi"
    ]
   },
   {