From d6f147bb46c47cc5f885b72536f5adbe6039af77 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 9 Dec 2012 04:22:37 -0500
Subject: [PATCH] Fix an off-by-one error in Euler's method.

---
 src/ODE/IVP.hs | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/ODE/IVP.hs b/src/ODE/IVP.hs
index 5d715a6..233e5f8 100644
--- a/src/ODE/IVP.hs
+++ b/src/ODE/IVP.hs
@@ -56,6 +56,8 @@ eulers_method1 x0 y0 f h =
 --   >>> let yN = head $ reverse ys
 --   >>> abs ((exp 1) - yN) < 1/10^3
 --   True
+--   >>> head ys == y0
+--   True
 --
 eulers_method :: forall a b c. (RealFrac a, RealFrac b, Integral c)
                => a -- ^ x0, the initial point
@@ -65,7 +67,7 @@ eulers_method :: forall a b c. (RealFrac a, RealFrac b, Integral c)
                -> c -- ^ n, the number of intervals to use.
                -> [b]
 eulers_method x0 y0 xN f n =
-  go xs y0 f
+  y0 : go xs y0 f
   where
     xs = partition n x0 xN
 
-- 
2.43.2