partially fixed (not enough order of convergence)

src/Numerics/OdeSolvers/AdamsBashforth.cs

@@ -65,19 +65,22 @@ namespace MathNet.Numerics.OdeSolvers
         /// <param name="N">Number of subintervals</param>
         /// <param name="f">ode model</param>
         /// <returns></returns>
-        public static double[] SecondOrder(double y0, double y1, double start, double end, int N, Func<double, double, double> f)
+        public static double[] SecondOrder(double y0,  double start, double end, int N, Func<double, double, double> f)
         {
             double dt = (end - start) / (N - 1);
             double t = start;
             double[] y = new double[N];
+            double k1 = f(t, y0);
+            double k2 = f(t + dt, y0 + dt * k1);
+            double y1 = y0 + 0.5 * dt * (k1 + k2);
             y[0] = y0;
+            t += dt;
             y[1] = y1;
             for (int i = 2; i < N; i++)
             {
-                y1 = f(t + dt, y1);
                 y[i] = y1 + dt * (1.5 * f(t + dt, y1) - 0.5 * f(t, y0));
                 t += dt;
-                y0 = y1;
+                y0 = y[i-1];
                 y1 = y[i];
             }
             return y;

src/UnitTests/OdeSolvers/OdeSolverTest.cs

@@ -72,9 +72,7 @@ namespace MathNet.Numerics.UnitTests.OdeSolvers
             for (int k = 0; k < 4; k++)
             {
                 double y0 = 0;
-                int N = Convert.ToInt32(Math.Pow(2, k + 6));
-                double dt = 2.0 / (N - 1);
-                double[] y_t = AdamsBashforth.SecondOrder(y0, sol(dt), 0, 2, N, ode);
+                double[] y_t = AdamsBashforth.SecondOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 6)), ode);
                 error = Math.Abs(sol(2) - y_t.Last());
                 if (oldError != 0)
                     ratio = Math.Log(oldError / error, 2);