From b1c955337ffb4e3fa76db90db2d1bda29ba60c17 Mon Sep 17 00:00:00 2001
From: Henry <Henry>
Date: Sun, 3 Nov 2013 16:03:03 +0000
Subject: [PATCH] ODESolvers/RKF45: Error evaluation is now consistent with the
 other RK solvers

---
 src/ODE/ODESolvers/RKF45/RKF45.C | 28 ++++++++++++----------------
 src/ODE/ODESolvers/RKF45/RKF45.H | 20 ++++++++++----------
 2 files changed, 22 insertions(+), 26 deletions(-)

diff --git a/src/ODE/ODESolvers/RKF45/RKF45.C b/src/ODE/ODESolvers/RKF45/RKF45.C
index b5324e049b..661c618255 100644
--- a/src/ODE/ODESolvers/RKF45/RKF45.C
+++ b/src/ODE/ODESolvers/RKF45/RKF45.C
@@ -56,19 +56,17 @@ const scalar
     RKF45::a64 = 1859.0/4104.0,
     RKF45::a65 = -11.0/40.0,
 
-    RKF45::b41  = 25.0/216.0,
-    RKF45::b42  = 0.0,
-    RKF45::b43  = 1408.0/2565.0,
-    RKF45::b44  = 2197.0/4104.0,
-    RKF45::b45  = -1.0/5.0,
-    RKF45::b46  = 0.0,
+    RKF45::b1  = 16.0/135.0,
+    RKF45::b3  = 6656.0/12825.0,
+    RKF45::b4  = 28561.0/56430.0,
+    RKF45::b5  = -9.0/50.0,
+    RKF45::b6  = 2.0/55.0,
 
-    RKF45::b51  = 16.0/135.0,
-    RKF45::b52  = 0.0,
-    RKF45::b53  = 6656.0/12825.0,
-    RKF45::b54  = 28561.0/56430.0,
-    RKF45::b55  = -9.0/50.0,
-    RKF45::b56  = 2.0/55.0;
+    RKF45::e1  = 25.0/216.0 - RKF45::b1,
+    RKF45::e3  = 1408.0/2565.0 - RKF45::b3,
+    RKF45::e4  = 2197.0/4104.0 - RKF45::b4,
+    RKF45::e5  = -1.0/5.0 - RKF45::b5,
+    RKF45::e6  = -RKF45::b6;
 }
 
 
@@ -143,7 +141,7 @@ Foam::scalar Foam::RKF45::solve
     {
         y[i] = y0[i]
           + dx
-           *(b51*dydx0[i] + b53*k3_[i] + b54*k4_[i] + b55*k5_[i] + b56*k6_[i]);
+           *(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b5*k5_[i] + b6*k6_[i]);
     }
 
     // Calculate the error estimate from the difference between the
@@ -152,9 +150,7 @@ Foam::scalar Foam::RKF45::solve
     {
         err_[i] =
             dx
-           *(b41*dydx0[i] + b43*k3_[i] + b44*k4_[i] + b45*k5_[i])
-          - (y[i] - y0[i])
-        ;
+           *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]);
     }
 
     return normalizeError(y0, y, err_);
diff --git a/src/ODE/ODESolvers/RKF45/RKF45.H b/src/ODE/ODESolvers/RKF45/RKF45.H
index 34a53d0fb0..442d9d3f4e 100644
--- a/src/ODE/ODESolvers/RKF45/RKF45.H
+++ b/src/ODE/ODESolvers/RKF45/RKF45.H
@@ -31,15 +31,15 @@ Description
     \verbatim
         "Low-order classical Runge-Kutta formulas with step size control
          and their application to some heat transfer problems."
-         Fehlberg, E.,
-         NASA Technical Report 315 1969
+        Fehlberg, E.,
+        NASA Technical Report 315, 1969.
 
-         "Solving Ordinary Differential Equations I: Nonstiff Problems,
-          second edition",
-         Hairer, E.,
-         Nørsett, S.,
-         Wanner, G.,
-         Springer-Verlag, Berlin. 1993, ISBN 3-540-56670-8.
+        "Solving Ordinary Differential Equations I: Nonstiff Problems,
+         second edition",
+        Hairer, E.,
+        Nørsett, S.,
+        Wanner, G.,
+        Springer-Verlag, Berlin. 1993, ISBN 3-540-56670-8.
     \endverbatim
 
     This method embedds the 4-th order integration step into the 5-th order step
@@ -112,8 +112,8 @@ class RKF45
             c2, c3, c4, c5, c6,
             a21, a31, a32, a41, a42, a43, a51, a52, a53, a54,
             a61, a62, a63, a64, a65,
-            b41, b42, b43, b44, b45, b46,
-            b51, b52, b53, b54, b55, b56;
+            b1, b3, b4, b5, b6,
+            e1, e3, e4, e5, e6;
 
 
         // Temporary fields