Add real sixth order method by Blanes 2002

Prog/splittings.f90

@@ -444,5 +444,38 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     splits(35)%Vcoeffs(4) = beta*conjg(alpha)
     splits(35)%Vcoeffs(5) = beta*alpha
 
+    ! The real sixth order method from Blanes 2002
+    call createsplit(splits(36), 11, 11)
+    splits(36)%Tcoeffs(1) = 0.0502627644003922
+    splits(36)%Tcoeffs(2) = 0.413514300428344
+    splits(36)%Tcoeffs(3) = 0.0450798897943977
+    splits(36)%Tcoeffs(4) = - 0.188054853819569
+    splits(36)%Tcoeffs(5) = 0.541960678450780
+
+    splits(36)%Tcoeffs(6) = 1.D0 - 2.D0 * &
+    & (splits(36)%Tcoeffs(1)+splits(36)%Tcoeffs(2)+splits(36)%Tcoeffs(3) +splits(36)%Tcoeffs(4) + splits(36)%Tcoeffs(5))
+
+    splits(36)%Tcoeffs(7) = splits(36)%Tcoeffs(5)
+    splits(36)%Tcoeffs(8) = splits(36)%Tcoeffs(4)
+    splits(36)%Tcoeffs(9) = splits(36)%Tcoeffs(3)
+    splits(36)%Tcoeffs(10) = splits(36)%Tcoeffs(2)
+    splits(36)%Tcoeffs(11) = splits(36)%Tcoeffs(1)
+
+
+    splits(36)%Vcoeffs(1) = 0.0
+    splits(36)%Vcoeffs(2) = 0.148816447901042
+    splits(36)%Vcoeffs(3) = - 0.132385865767784
+    splits(36)%Vcoeffs(4) = 0.067307604692185
+    splits(36)%Vcoeffs(5) = 0.432666402578175
+    splits(36)%Vcoeffs(6) = 1.D0/2.D0-&
+    & (splits(36)%Vcoeffs(2)+splits(36)%Vcoeffs(3)+splits(36)%Vcoeffs(4)+splits(36)%Vcoeffs(5) )
+    splits(36)%Vcoeffs(7) = splits(36)%Vcoeffs(6)
+    splits(36)%Vcoeffs(8) = splits(36)%Vcoeffs(5)
+    splits(36)%Vcoeffs(9) = splits(36)%Vcoeffs(4)
+    splits(36)%Vcoeffs(10) = splits(36)%Vcoeffs(3)
+    splits(36)%Vcoeffs(11) = splits(36)%Vcoeffs(2)
+
+
+
 end subroutine
 end module splittings