X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FODE%2FIVP.hs;h=5bffe08cfff387210c3bdd7cc3f5483dba81c13e;hb=e1bf90ef57aaa37620e001d04cabec0ea2e8ddbf;hp=615c668367bd6a26e22567ed0f70a0f90da6e7c0;hpb=2f54e89d36e835c58efcc281741632d457859b20;p=numerical-analysis.git

diff --git a/src/ODE/IVP.hs b/src/ODE/IVP.hs
index 615c668..5bffe08 100644
--- a/src/ODE/IVP.hs
+++ b/src/ODE/IVP.hs
@@ -9,15 +9,18 @@
 --   for x in [x0, xN].
 --
 
-module ODE.IVP
+module ODE.IVP (
+  eulers_method,
+  eulers_method1,
+  eulers_methodH )
 where
 
-import Misc (partition)
-import NumericPrelude hiding (abs)
-import qualified Algebra.Field as Field
-import qualified Algebra.ToInteger as ToInteger
-import qualified Algebra.ToRational as ToRational
-import qualified Algebra.RealField as RealField
+import Misc ( partition )
+import NumericPrelude hiding ( abs )
+import qualified Algebra.Field as Field ( C )
+import qualified Algebra.ToInteger as ToInteger ( C )
+import qualified Algebra.ToRational as ToRational ( C )
+import qualified Algebra.RealField as RealField ( C )
 
 -- | A single iteration of Euler's method over the interval
 --   [$x0$, $x0$+$h$].
@@ -31,7 +34,7 @@ import qualified Algebra.RealField as RealField
 --   >>> eulers_method1 x0 y0 f h
 --   2.0
 --
-eulers_method1 :: (Field.C a, ToRational.C a, Field.C b)
+eulers_method1 :: forall a b. (Field.C a, ToRational.C a, Field.C b)
                => a -- ^ x0, the initial point
                -> b -- ^ y0, the initial value at x0
                -> (a -> b -> b) -- ^ The function f(x,y)
@@ -40,7 +43,7 @@ eulers_method1 :: (Field.C a, ToRational.C a, Field.C b)
 eulers_method1 x0 y0 f h =
   y0 +  h'*y'
   where
-    h' = fromRational'$ toRational h
+    h' = fromRational'$ toRational h :: b
     y' = (f x0 y0)