Reimplementierung für DGlS

heun.py

@@ -1,22 +1,50 @@
 # Verfahren von Heun zur numerischen Lösung von Anfangswertaufgaben.
-
-def heun(xk,yk,h,ys):
-    xk1 = xk + h
-    yk1p = yk + h * ys(xk,yk)
-    yk1 = 0.5*(yk+yk1p+h*ys(xk1,yk1p))
-    return (xk1,yk1p)
+#
+#def heun(xk,yk,h,ys):
+#    xk1 = xk + h
+#    yk1p = yk + h * ys(xk,yk)
+#    yk1 = 0.5*(yk+yk1p+h*ys(xk1,yk1p))
+#    return (xk1,yk1p)
+#
+#def run_heun(K,h,x0,y0,ys):
+#    if not isinstance(ys,list): ys = [ys]
+#    if not isinstance(y0,list): y0 = [y0]
+#    xk = x0
+#    yk = y0
+#    xks = x0
+#    yks = [ [v] for v in y0 ]
+#
+#    for i in range(K):
+#        for j in range(len(ys)):
+#            xk,yk[j] = heun(xk,yk[j],h,ys[i])
+#            xks.append(xk)
+#            yks[j].append(yk[j])
+#
 
 def run_heun(K,h,x0,y0,ys):
-    if not isinstance(ys,list): ys = [ys]
     if not isinstance(y0,list): y0 = [y0]
+    if not isinstance(ys,list): ys = [ys]
+
     xk = x0
     yk = y0
-    xks = x0
+    xka = 0
+    yka = [0]*len(yk)
+    ykp = [0]*len(yk)
+
+    xks = [x0]
     yks = [ [v] for v in y0 ]
 
     for i in range(K):
+        xka = xk + h
+        xks.append(xka)
         for j in range(len(ys)):
-            xk,yk[j] = heun(xk,yk[j],h,ys[i])
-            xks.append(xk)
-            yks[j].append(yk[j])
+            yka[j] = yk[j] + h * ys[j](xk,*yk)
+        for j in range(len(ys)):
+            ykp[j] = 0.5*(yk[j] + yka[j] + h * ys[j](xka,*yka))
+            yks[j].append(ykp[j])
+        yk = ykp
+        xk = xka
+
+    return [xks] + yks
+