added explicit euler's method (#1394)

* added explicit euler's method

* update explicit_euler.py variable names

maths/explicit_euler.py

@@ -0,0 +1,41 @@
+import numpy as np
+
+
+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:
+    ode_func -- The ode as a function of x and y
+    y0 -- the initial value for y
+    x0 -- the initial value for x
+    stepsize -- the increment value for x
+    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)/stepsize))
+    y = np.zeros((N + 1,))
+    y[0] = y0
+    x = x0
+
+    for k in range(N):
+        y[k + 1] = y[k] + stepsize*ode_func(x, y[k])
+        x += stepsize
+
+    return y
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+