--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+time/+rk/rungekutta_6.m	Thu Nov 15 16:42:58 2018 -0800
@@ -0,0 +1,31 @@
+% Takes one time step of size k using the rungekutta method
+% starting from v_0 and where the function F(v,t) gives the
+% time derivatives.
+function v = rungekutta_6(v, t , k, F)
+    s = 7
+    k = zeros(length(v),s)
+    a = zeros(7,6);
+    c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
+    b = [1/12, 0, 0, 0, 5/12, 5/12, 1/12];
+    a = [
+        0,                           0,                          0,                       0,                     0,                 0;
+        4/7,                         0,                          0,                       0,                     0,                 0;
+        115/112,                     -5/16,                      0,                       0,                     0,                 0;
+        589/630,                     5/18,                       -16/45,                  0,                     0,                 0;
+        229/1200 - 29/6000*sqrt(5),  119/240 - 187/1200*sqrt(5), -14/75 + 34/375*sqrt(5), -3/100*sqrt(5),        0,                 0;
+        71/2400 - 587/12000*sqrt(5), 187/480 - 391/2400*sqrt(5), -38/75 + 26/375*sqrt(5), 27/80 - 3/400*sqrt(5), (1+sqrt(5))/4,     0;
+        -49/480 + 43/160*sqrt(5),    -425/96 + 51/32*sqrt(5),    52/15 - 4/5*sqrt(5),     -27/16 + 3/16*sqrt(5), 5/4 - 3/4*sqrt(5), 5/2 - 1/2*sqrt(5);
+    ]
+
+    for i = 1:s
+        u = v
+        for j = 1: i-1
+            u = u + h*a(i,j) * k(:,j)
+        end
+        k(:,i) = F(t+c(i)*k,u)
+    end
+
+    for i = 1:s
+        v = v + k*b(i)*k(:,i)
+    end
+end