--- gsl-1.2/ode-initval/rk8pd.c~	Mon Nov 19 22:39:32 2001
+++ gsl-1.2/ode-initval/rk8pd.c	Wed Oct  9 09:49:26 2002
@@ -17,7 +17,12 @@
  * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  */
 
-/* Runge-Kutta 8(9), Prince-Dormand */
+/* Runge-Kutta 8(7), Prince-Dormand
+ * The original article is :
+ *  High order embedded Runge-Kutta formulae
+ *  P.J. Prince and J.R. Dormand
+ *  Journal of Computational and Applied Mathematics, volume 7, no. 1, 1981
+ */
 
 /* Author:  G. Jungman
  */
@@ -80,14 +85,21 @@
 static const double b4[] = { 1.0 / 32.0, 0.0, 3.0 / 32.0 };
 static const double b5[] = { 5.0 / 16.0, 0.0, -75.0 / 64.0, 75.0 / 64.0 };
 static const double b6[] = { 3.0 / 80.0, 0.0, 0.0, 3.0 / 16.0, 3.0 / 20.0 };
+
+/* the b7[0] and b7[3] coefficients were corrected by Luc Maisonobe
+ * since the approximation given in the original article seemed to be
+ * wrong, because the sum b7[0]+b7[1]+ ... +b7[5] was not equal to
+ * ah[5] as it should be.
+ */
 static const double b7[] = {
-  29443841.0 / 614563906.0,
+  215595617.0 / 4500000000.0, /* was 29443841/614563906 in the article */
   0.0,
   0.0,
-  77736538.0 / 692538347.0,
+  202047683.0 / 1800000000.0, /* was 77736538/692538347 in the article */
   -28693883.0 / 1125000000.0,
   23124283.0 / 1800000000.0
 };
+
 static const double b8[] = {
   16016141.0 / 946692911.0,
   0.0,