From a8f5e56f0afbc8fc2b950af61ea3780d0f1d99e5 Mon Sep 17 00:00:00 2001
From: Stephen Ryan <24819660+infrontoftheforest@users.noreply.github.com>
Date: Fri, 18 Oct 2019 17:39:22 +0200
Subject: [PATCH 1/2] added explicit euler's method

---
 maths/explicit_euler.py | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 maths/explicit_euler.py

diff --git a/maths/explicit_euler.py b/maths/explicit_euler.py
new file mode 100644
index 000000000000..17e6a34da666
--- /dev/null
+++ b/maths/explicit_euler.py
@@ -0,0 +1,41 @@
+import numpy as np
+
+
+def explicit_euler(f, y0, x0, h, x_end):
+    """
+    Calculate numeric solution at each step to an ODE using Euler's Method
+
+    https://en.wikipedia.org/wiki/Euler_method
+
+    Arguments:
+    f -- The ode as a function of x and y
+    y0 -- the initial value for y
+    x0 -- the initial value for x
+    h -- the stepsize
+    x_end -- the end value for x
+
+    >>> # the exact solution is math.exp(x)
+    >>> def f(x, y):
+    ...     return y
+    >>> y0 = 1
+    >>> y = explicit_euler(f, y0, 0.0, 0.01, 5)
+    >>> y[-1]
+    144.77277243257308
+    """
+    N = int(np.ceil((x_end - x0)/h))
+    y = np.zeros((N + 1,))
+    y[0] = y0
+    x = x0
+
+    for k in range(N):
+        y[k + 1] = y[k] + h*f(x, y[k])
+        x += h
+
+    return y
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+

From 8c2e748a7c6783225ace7a275d7e805926eeee41 Mon Sep 17 00:00:00 2001
From: Stephen <24819660+infrontoftheforest@users.noreply.github.com>
Date: Mon, 21 Oct 2019 17:12:05 +0000
Subject: [PATCH 2/2] update explicit_euler.py variable names

---
 maths/explicit_euler.py | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/maths/explicit_euler.py b/maths/explicit_euler.py
index 17e6a34da666..9fce4e4185a6 100644
--- a/maths/explicit_euler.py
+++ b/maths/explicit_euler.py
@@ -1,17 +1,17 @@
 import numpy as np
 
 
-def explicit_euler(f, y0, x0, h, x_end):
+def explicit_euler(ode_func, y0, x0, stepsize, x_end):
     """
     Calculate numeric solution at each step to an ODE using Euler's Method
 
     https://en.wikipedia.org/wiki/Euler_method
 
     Arguments:
-    f -- The ode as a function of x and y
+    ode_func -- The ode as a function of x and y
     y0 -- the initial value for y
     x0 -- the initial value for x
-    h -- the stepsize
+    stepsize -- the increment value for x
     x_end -- the end value for x
 
     >>> # the exact solution is math.exp(x)
@@ -22,14 +22,14 @@ def explicit_euler(f, y0, x0, h, x_end):
     >>> y[-1]
     144.77277243257308
     """
-    N = int(np.ceil((x_end - x0)/h))
+    N = int(np.ceil((x_end - x0)/stepsize))
     y = np.zeros((N + 1,))
     y[0] = y0
     x = x0
 
     for k in range(N):
-        y[k + 1] = y[k] + h*f(x, y[k])
-        x += h
+        y[k + 1] = y[k] + stepsize*ode_func(x, y[k])
+        x += stepsize
 
     return y