From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 9 Dec 2012 09:22:37 +0000 (-0500)
Subject: Fix an off-by-one error in Euler's method.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=commitdiff_plain;h=d6f147bb46c47cc5f885b72536f5adbe6039af77

Fix an off-by-one error in Euler's method.
---

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