From 0d4e770dc06763d225dce66f82bd49b052bead06 Mon Sep 17 00:00:00 2001
From: Christian Kolset <christian.kolset@gmail.com>
Date: Fri, 9 May 2025 09:53:20 -0600
Subject: Added auto-generated (md converted) notebooks to modules. Added
 module 3 tutorials

---
 tutorials/module_3/ForwardFiniteDifference | 37 ++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)
 create mode 100644 tutorials/module_3/ForwardFiniteDifference

(limited to 'tutorials/module_3/ForwardFiniteDifference')

diff --git a/tutorials/module_3/ForwardFiniteDifference b/tutorials/module_3/ForwardFiniteDifference
new file mode 100644
index 0000000..128bb56
--- /dev/null
+++ b/tutorials/module_3/ForwardFiniteDifference
@@ -0,0 +1,37 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu May  8 13:27:05 2025
+
+@author: christian
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+
+# step size
+h = 0.1
+# define grid
+x = np.arange(0, 2*np.pi, h)
+# compute function
+y = np.cos(x) 
+
+# compute vector of forward differences
+forward_diff = np.diff(y)/h 
+# compute corresponding grid
+x_diff = x[:-1:] 
+# compute exact solution
+exact_solution = -np.sin(x_diff) 
+
+# Plot solution
+plt.figure(figsize = (12, 8))
+plt.plot(x_diff, forward_diff, '--', \
+         label = 'Finite difference approximation')
+plt.plot(x_diff, exact_solution, \
+         label = 'Exact solution')
+plt.legend()
+plt.show()
+
+# Compute max error between 
+# numerical derivative and exact solution
+max_error = max(abs(exact_solution - forward_diff))
+print(max_error)
\ No newline at end of file
-- 
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