2016 Update

Task/Euler-method/Haskell/euler-method-1.hs

@@ -0,0 +1,5 @@
+-- the solver
+dsolveBy _ _ [] _ = error "empty solution interval"
+dsolveBy method f mesh x0 = zip mesh results
+  where results = scanl (method f) x0 intervals
+        intervals = zip mesh (tail mesh)

Task/Euler-method/Haskell/euler-method-2.hs

@@ -0,0 +1,14 @@
+-- 1-st order Euler
+euler f x (t1,t2) = x + (t2 - t1) * f t1 x
+
+-- 2-nd order Runge-Kutta
+rk2 f x (t1,t2) = x + h * f (t1 + h/2) (x + h/2*f t1 x)
+  where h = t2 - t1
+
+-- 4-th order Runge-Kutta
+rk4 f x (t1,t2) = x + h/6 * (k1 + 2*k2 + 2*k3 + k4)
+  where k1 = f t1 x
+        k2 = f (t1 + h/2) (x + h/2*k1)
+        k3 = f (t1 + h/2) (x + h/2*k2)
+        k4 = f (t1 + h) (x + h*k3)
+        h = t2 - t1

Task/Euler-method/Haskell/euler-method-3.hs

@@ -0,0 +1,23 @@
+import Graphics.EasyPlot
+
+newton t temp = -0.07 * (temp - 20)
+
+exactSolution t = 80*exp(-0.07*t)+20
+
+test1 = plot (PNG "euler1.png")
+  [ Data2D [Title "Step 10", Style Lines] [] sol1
+  , Data2D [Title "Step 5", Style Lines] [] sol2
+  , Data2D [Title "Step 1", Style Lines] [] sol3
+  , Function2D [Title "exact solution"] [Range 0 100] exactSolution ]
+ where sol1 = dsolveBy euler newton [0,10..100] 100
+       sol2 = dsolveBy euler newton [0,5..100] 100
+       sol3 = dsolveBy euler newton [0,1..100] 100
+
+test2 = plot (PNG "euler2.png")
+  [ Data2D [Title "Euler"] [] sol1
+  , Data2D [Title "RK2"] [] sol2
+  , Data2D [Title "RK4"] [] sol3
+  , Function2D [Title "exact solution"] [Range 0 100] exactSolution ]
+ where sol1 = dsolveBy euler newton [0,10..100] 100
+       sol2 = dsolveBy rk2 newton [0,10..100] 100
+       sol3 = dsolveBy rk4 newton [0,10..100] 100

Task/Euler-method/Haskell/euler-method.hs

@@ -1,15 +0,0 @@
-import Text.Printf
-
-euler :: (Num a, Ord a) => (a -> a -> a) -> a -> a -> a -> a -> [(a,a)]
-euler f y0 a b h =
-	(a, y0) :
-	if a < b
-		then euler f (y0 + (f a y0) * h) (a + h) b h
-		else []
-
-newtonCooling :: Double -> Double -> Double
-newtonCooling _ t = -0.07 * (t - 20)
-
-main = do
-  mapM_ (uncurry $ printf "%6.3f %6.3f\n") $ euler newtonCooling 100 0 100 10
-  putStrLn "DONE"