fix more methods

Prog/splittings.f90

@@ -66,11 +66,12 @@ subroutine init_splittings(split)
     splits(2)%Vcoeffs(1) = 1.0
 
     !T-V-T leapfrog
-    call createsplit(splits(3), 2, 1)
+    call createsplit(splits(3), 2, 2)
     splits(3)%Tcoeffs(1) = 0.5
     splits(3)%Tcoeffs(2) = 0.5
 
-    splits(3)%Vcoeffs(1) = 1.0
+    splits(3)%Vcoeffs(1) = 0.0
+    splits(3)%Vcoeffs(2) = 1.0
 
     !V-T-V leapfrog
     call createsplit(splits(4), 2, 2)
@@ -87,9 +88,9 @@ subroutine init_splittings(split)
     splits(5)%Tcoeffs(2) = (1.0 - 2*0.1931833275037836)
     splits(5)%Tcoeffs(3) = 0.1931833275037836
 
-    splits(5)%Vcoeffs(1) = 0.5
+    splits(5)%Vcoeffs(1) = 0.0
     splits(5)%Vcoeffs(2) = 0.5
-    splits(5)%Vcoeffs(3) = 0.0
+    splits(5)%Vcoeffs(3) = 0.5
 
     ! S_6 4 from http://personales.upv.es/serblaza/2011EncyclopediaSplittingMethods.pdf
 
@@ -166,10 +167,10 @@ 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)
@@ -270,10 +271,10 @@ subroutine init_splittings(split)
     splits(24)%Tcoeffs(3) = splits(24)%Tcoeffs(2)
     splits(24)%Tcoeffs(4) = splits(24)%Tcoeffs(1)
 
-    splits(24)%Vcoeffs(1) = beta
-    splits(24)%Vcoeffs(2) = 1.D0 - 2.D0*beta
-    splits(24)%Vcoeffs(3) = beta
-    splits(24)%Vcoeffs(4) = 0.D0
+    splits(24)%Vcoeffs(1) = 0.0
+    splits(24)%Vcoeffs(2) = beta
+    splits(24)%Vcoeffs(3) = 1.D0 - 2.D0*beta
+    splits(24)%Vcoeffs(4) = beta
 
     ! the variant with m=4 optimized for large step sizes in Blanes 2014, 2. Order
     call createsplit(splits(25), 5, 5)
@@ -287,21 +288,22 @@ subroutine init_splittings(split)
     splits(25)%Tcoeffs(4) = splits(25)%Tcoeffs(2)
     splits(25)%Tcoeffs(5) = splits(25)%Tcoeffs(1)
 
-    splits(25)%Vcoeffs(1) = chi
-    splits(25)%Vcoeffs(2) = 1.D0/2.D0 - chi
-    splits(25)%Vcoeffs(3) = splits(25)%Vcoeffs(2)
-    splits(25)%Vcoeffs(4) = splits(25)%Vcoeffs(1)
-    splits(25)%Vcoeffs(5) = 0.D0
+    splits(25)%Vcoeffs(1) = 0.0
+    splits(25)%Vcoeffs(2) = chi
+    splits(25)%Vcoeffs(3) = 1.D0/2.D0 - chi
+    splits(25)%Vcoeffs(4) = splits(25)%Vcoeffs(3)
+    splits(25)%Vcoeffs(5) = splits(25)%Vcoeffs(2)
 
-    call createsplit(splits(26), 3, 2) !hermitian third order method with entirely complex coefficients
+    call createsplit(splits(26), 3, 3) !hermitian third order method with entirely complex coefficients, find the paper by Blanes I think...
     alpha = CMPLX(1.D0/2.D0, Sqrt(3.D0)/6.D0, kind=kind(0.D0))
     beta = 1.D0-alpha
     splits(26)%Tcoeffs(1) = alpha/2.D0
     splits(26)%Tcoeffs(2) = 1.D0/2.D0
     splits(26)%Tcoeffs(3) = conjg(splits(26)%Tcoeffs(1))
 
-    splits(26)%Vcoeffs(1) = alpha
-    splits(26)%Vcoeffs(2) = conjg(alpha)
+    splits(26)%Vcoeffs(1) = 0.0
+    splits(26)%Vcoeffs(2) = alpha
+    splits(26)%Vcoeffs(3) = conjg(alpha)
 
     ! The simple Order-4 method from here: http://www.gicas.uji.es/Research/splitting-complex.html
     call createsplit(splits(27), 5, 5)
@@ -312,10 +314,8 @@ subroutine init_splittings(split)
     splits(27)%Tcoeffs(4) = CMPLX(4.D0/15, +2.D0/15, kind=kind(0.D0))
     splits(27)%Tcoeffs(5) = CMPLX(1.D0/10, -1.D0/30, kind=kind(0.D0))
 
-    splits(27)%Vcoeffs(1) = 1.D0/4.D0
-    splits(27)%Vcoeffs(2) = 1.D0/4.D0
-    splits(27)%Vcoeffs(3) = 1.D0/4.D0
-    splits(27)%Vcoeffs(4) = 1.D0/4.D0
+    splits(27)%Vcoeffs(1) = 0.0
+    splits(27)%Vcoeffs = 1.D0/4.D0
 
     ! The optimized Order-4 method from here: http://www.gicas.uji.es/Research/splitting-complex.html
     call createsplit(splits(28), 5, 5)
@@ -350,6 +350,7 @@ subroutine init_splittings(split)
     call createsplit(splits(30), 17, 17)
     splits(30)%Vcoeffs = 1.D0/16
     splits(30)%Vcoeffs(1) = 0
+
 splits(30)%Tcoeffs(1)=CMPLX(0.0246948760870180646409108649968422478386,-0.0078747955629068770581715779495269421632, dp)
 splits(30)%Tcoeffs(2)=CMPLX(0.0638134740213026997793663041882001469632, 0.0353657610341433278046294046497147418127, dp)
 splits(30)%Tcoeffs(3)=CMPLX(0.0684250940303164419703970078217446840585,-0.0622622444507486769953325406444475960461, dp)
@@ -371,8 +372,8 @@ splits(30)%Tcoeffs(17) = splits(30)%Tcoeffs(1)
     ! My first own second order method, designed to be a hermitian sequence of Operators
     call createsplit(splits(31), 4, 4)
     beta = 1.D0/3.D0
-    splits(31)%Tcoeffs(1) = CMPLX(1.D0/4, -1.D0/6.D0, dp)
-    splits(31)%Tcoeffs(2) = CMPLX(1.D0/4,1.D0/2.D0, dp)
+    splits(31)%Tcoeffs(1) = CMPLX(1.D0/4.D0, -1.D0/6.D0, dp)
+    splits(31)%Tcoeffs(2) = CMPLX(1.D0/4.D0, 1.D0/2.D0, dp)
     splits(31)%Tcoeffs(3) = conjg(splits(31)%Tcoeffs(2))
     splits(31)%Tcoeffs(4) = conjg(splits(31)%Tcoeffs(1))