--- a/liboctave/LSODE-opts.in
+++ b/liboctave/LSODE-opts.in
@@ -4,6 +4,10 @@
 
 OPTION
   NAME = "absolute tolerance"
+  DOC_ITEM
+Absolute tolerance.  May be either vector or scalar.  If a vector, it
+must match the dimension of the state vector.
+  END_DOC_ITEM
   TYPE = "Array<double>"
   SET_ARG_TYPE = "const $TYPE&"
   INIT_BODY
@@ -24,7 +28,39 @@
 END_OPTION
 
 OPTION
+  NAME = "relative tolerance"
+  DOC_ITEM
+Relative tolerance parameter.  Unlike the absolute tolerance, this
+parameter may only be a scalar.
+
+The local error test applied at each integration step is
+
+@example
+  abs (local error in x(i)) <= rtol * abs (y(i)) + atol(i)
+@end example
+  END_DOC_ITEM
+  TYPE = "double"
+  INIT_VALUE = "::sqrt (DBL_EPSILON)"
+  SET_EXPR = "(val > 0.0) ? val : ::sqrt (DBL_EPSILON)"
+END_OPTION
+
+OPTION
   NAME = "integration method"
+A string specifing the method of integration to use to solve the ODE
+system.  Valid values are
+
+@table @asis
+@item \"adams\"
+@itemx \"non-stiff\"
+No Jacobian used (even if it is available).
+@item \"bdf\"
+@item \"stiff\"
+Use stiff backward differentiation formula (BDF) method.  If a
+function to compute the Jacobian is not supplied, @code{lsode} will
+compute a finite difference approximation of the Jacobian matrix.
+@end table
+  DOC_ITEM
+  END_DOC_ITEM
   TYPE = "std::string"
   SET_ARG_TYPE = "const $TYPE&"
   INIT_VALUE = ""stiff""
@@ -41,6 +77,10 @@
 
 OPTION
   NAME = "initial step size"
+  DOC_ITEM
+The step size to be attempted on the first step (default is determined
+automatically).
+  END_DOC_ITEM
   TYPE = "double"
   INIT_VALUE = "-1.0"
   SET_EXPR = "(val >= 0.0) ? val : -1.0"
@@ -48,6 +88,10 @@
 
 OPTION
   NAME = "maximum step size"
+  DOC_ITEM
+Setting the maximum stepsize will avoid passing over very large
+regions  (default is not specified).
+  END_DOC_ITEM
   TYPE = "double"
   INIT_VALUE = "-1.0"
   SET_EXPR = "(val >= 0.0) ? val : -1.0"
@@ -55,20 +99,19 @@
 
 OPTION
   NAME = "minimum step size"
+  DOC_ITEM
+The minimum absolute step size allowed (default is 0).
+  END_DOC_ITEM
   TYPE = "double"
   INIT_VALUE = "0.0"
   SET_EXPR = "(val >= 0.0) ? val : 0.0"
 END_OPTION
 
 OPTION
-  NAME = "relative tolerance"
-  TYPE = "double"
-  INIT_VALUE = "::sqrt (DBL_EPSILON)"
-  SET_EXPR = "(val > 0.0) ? val : ::sqrt (DBL_EPSILON)"
-END_OPTION
-
-OPTION
   NAME = "step limit"
+  DOC_ITEM
+Maximum number of steps allowed (default is 100000).
+  END_DOC_ITEM
   TYPE = "int"
   INIT_VALUE = "100000"
   SET_EXPR = "val"