Initial Refactoring of yoshi_otter and Test Implementation

yoshi_otter/algebra/edo/__edo.py

@@ -0,0 +1,51 @@
+from typing import Callable
+
+
+class Edo:
+
+    def __init__(self, function: Callable[[float], float]) -> None:
+        self.F = function
+
+    def euler(self, a: float, y: float, b: float, n: int = 10**6) -> float:
+
+        dx = (b - a) / n
+
+        def x(i):
+            return a + i * dx
+
+        for i in range(n):
+            y = y + (self.F(x(i), y)) * dx
+
+        return y
+
+    def runge(self, a: float, y: float, b: float, n: int = 10**6) -> float:
+
+        dx = (b - a) / n
+
+        def x(i):
+            return a + i * dx
+
+        for i in range(n):
+            y = y + (dx / 2) * (self.F(x(i), y) + self.F(x(i + 1), (y + (dx * self.F(x(i), y)))))
+
+        return y
+
+    def adams(self, a: float, y: float, b: float, n: int = None
+              ) -> float:
+
+        if n is None:
+            n = 10 ** 6
+
+        dx = (b - a) / n
+
+        def x(i):
+            return a + i * dx
+
+        for i in range(n):
+            f0 = self.F(x(i), y)
+            f1 = self.F(x(i + 1), y + dx * self.F(x(i) + (dx / 2), y + (dx / 2) * self.F(x(i), y)))
+            f2 = self.F(x(i + 2), y + (dx / 2) * (3 * f1 - f0))
+
+            y += (dx / 12) * (5 * f2 + 8 * f1 - f0)
+
+        return y