fix the *classical* methods

Prog/splittings.f90

@@ -149,12 +149,13 @@ subroutine init_splittings(split)
     splits(9)%Tcoeffs(5) = splits(9)%Tcoeffs(2)
     splits(9)%Tcoeffs(6) = splits(9)%Tcoeffs(1)
 
-    splits(9)%Vcoeffs(1) = 2.D0/5
-    splits(9)%Vcoeffs(2) = -1.D0/10
-    splits(9)%Vcoeffs(3) = 1.D0 - 2*(splits(9)%Vcoeffs(1)+splits(9)%Vcoeffs(2))
-    splits(9)%Vcoeffs(4) = splits(9)%Vcoeffs(2)
-    splits(9)%Vcoeffs(5) = splits(9)%Vcoeffs(1)
-    splits(9)%Vcoeffs(6) = 0
+    splits(9)%Vcoeffs(1) = 0
+    splits(9)%Vcoeffs(2) = 2.D0/5
+    splits(9)%Vcoeffs(3) = -1.D0/10
+    splits(9)%Vcoeffs(4) = 1.D0 - 2*(splits(9)%Vcoeffs(1)+splits(9)%Vcoeffs(2))
+    splits(9)%Vcoeffs(5) = splits(9)%Vcoeffs(2)
+    splits(9)%Vcoeffs(6) = splits(9)%Vcoeffs(1)
+
 
     ! Symmetric from symmetric
     ! This coresponds to the classical Forest/Ruth algorithm
@@ -166,10 +167,11 @@ subroutine init_splittings(split)
     splits(10)%Tcoeffs(3) = splits(10)%Tcoeffs(2)
     splits(10)%Tcoeffs(4) = splits(10)%Tcoeffs(1)
 
-    splits(10)%Vcoeffs(1) = alpha
-    splits(10)%Vcoeffs(2) = beta
-    splits(10)%Vcoeffs(3) = alpha
-    splits(10)%Vcoeffs(4) = 0.0
+    splits(10)%Vcoeffs(1) = 0.0
+    splits(10)%Vcoeffs(2) = alpha
+    splits(10)%Vcoeffs(3) = beta
+    splits(10)%Vcoeffs(4) = alpha
+
 
     ! Another variant of symmetric with symmetric by Suzuki
     call createsplit(splits(11), 6, 6)
@@ -182,12 +184,13 @@ subroutine init_splittings(split)
     splits(11)%Tcoeffs(5) = splits(11)%Tcoeffs(2)
     splits(11)%Tcoeffs(6) = splits(11)%Tcoeffs(1)
 
-    splits(11)%Vcoeffs(1) = alpha
+    splits(11)%Vcoeffs(1) = 0
     splits(11)%Vcoeffs(2) = alpha
-    splits(11)%Vcoeffs(3) = beta
-    splits(11)%Vcoeffs(4) = splits(11)%Vcoeffs(2)
-    splits(11)%Vcoeffs(5) = splits(11)%Vcoeffs(1)
-    splits(11)%Vcoeffs(6) = 0
+    splits(11)%Vcoeffs(3) = alpha
+    splits(11)%Vcoeffs(4) = beta
+    splits(11)%Vcoeffs(5) = splits(11)%Vcoeffs(2)
+    splits(11)%Vcoeffs(6) = splits(11)%Vcoeffs(1)
+
 
     ! fourth order method from Omelyan, 2001, previously discovered by McLachlan 1995
     call createsplit(splits(12), 5, 5)