Added runge kutta integration.

matrix/integration.hpp

@@ -0,0 +1,26 @@
+#pragma once
+
+#include "math.hpp"
+
+namespace matrix {
+
+template<typename Type, size_t M>
+int integrate_rk4(
+	Vector<Type, M> (*f)(Type, Vector<Type, M>),
+    Vector<Type, M> & y,
+    Type & t,
+	Type h
+	)
+{
+	// https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
+	Vector<Type, M> k1, k2, k3, k4;
+   	k1 = f(t, y);
+   	k2 = f(t + h/2, y + k1*h/2);
+   	k3 = f(t + h/2, y + k2*h/2);
+   	k4 = f(t + h, y + k3*h);
+	y += (k1 + k2*2 + k3*2 + k4)*(h/6);
+	t += h;
+	return 0;
+}
+
+}; // namespace matrix