diff --git a/src/Numerics/Numerics.csproj b/src/Numerics/Numerics.csproj
index 6369d13e..2306ffa1 100644
--- a/src/Numerics/Numerics.csproj
+++ b/src/Numerics/Numerics.csproj
@@ -112,7 +112,8 @@
-
+
+
diff --git a/src/Numerics/OdeSolvers/AdamsBashforth.cs b/src/Numerics/OdeSolvers/AdamsBashforth.cs
new file mode 100644
index 00000000..0f731537
--- /dev/null
+++ b/src/Numerics/OdeSolvers/AdamsBashforth.cs
@@ -0,0 +1,166 @@
+//
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+//
+// Copyright (c) 2009-2016 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+//
+using System;
+
+namespace MathNet.Numerics.OdeSolvers
+{
+ public static class AdamsBashforth
+ {
+ ///
+ /// First Order AB method(same as Forward Euler)
+ ///
+ /// Initial value
+ /// Start Time
+ /// End Time
+ /// Size of output array(the larger, the finer)
+ /// ode model
+ /// approximation with size N
+ public static double[] FirstOrder(double y0, double start, double end, int N, Func f)
+ {
+ double dt = (end - start) / (N - 1);
+ double t = start;
+ double[] y = new double[N];
+ y[0] = y0;
+ for (int i = 1; i < N; i++)
+ {
+ y[i] = y0 + dt * f(t, y0);
+ t += dt;
+ y0 = y[i];
+ }
+ return y;
+ }
+
+ ///
+ /// Second Order AB Method
+ ///
+ /// Initial value 1
+ /// Start Time
+ /// End Time
+ /// Size of output array(the larger, the finer)
+ /// ode model
+ /// approximation with size N
+ public static double[] SecondOrder(double y0, double start, double end, int N, Func 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;
+ y[1] = y1;
+ for (int i = 2; i < N; i++)
+ {
+ y[i] = y1 + dt * (1.5 * f(t + dt, y1) - 0.5 * f(t, y0));
+ t += dt;
+ y0 = y[i - 1];
+ y1 = y[i];
+ }
+ return y;
+ }
+
+ ///
+ /// Third Order AB Method
+ ///
+ /// Initial value 1
+ /// Start Time
+ /// End Time
+ /// Size of output array(the larger, the finer)
+ /// ode model
+ /// approximation with size N
+ public static double[] ThirdOrder(double y0, double start, double end, int N, Func f)
+ {
+ double dt = (end - start) / (N - 1);
+ double t = start;
+ double[] y = new double[N];
+
+ double k1 = 0;
+ double k2 = 0;
+ double k3 = 0;
+ double k4 = 0;
+ y[0] = y0;
+ for (int i = 1; i < 3; i++)
+ {
+ k1 = dt * f(t, y0);
+ k2 = dt * f(t + dt / 2, y0 + k1 / 2);
+ k3 = dt * f(t + dt / 2, y0 + k2 / 2);
+ k4 = dt * f(t + dt, y0 + k3);
+ y[i] = y0 + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
+ t += dt;
+ y0 = y[i];
+ }
+ for (int i = 3; i < N; i++)
+ {
+ y[i] = y[i - 1] + dt * (23 * f(t, y[i - 1]) - 16 * f(t - dt, y[i - 2]) + 5 * f(t - 2 * dt, y[i - 3])) / 12.0;
+ t += dt;
+ }
+ return y;
+ }
+
+ ///
+ /// Fourth Order AB Method
+ ///
+ /// Initial value 1
+ /// Start Time
+ /// End Time
+ /// Size of output array(the larger, the finer)
+ /// ode model
+ /// approximation with size N
+ public static double[] FourthOrder(double y0, double start, double end, int N, Func f)
+ {
+ double dt = (end - start) / (N - 1);
+ double t = start;
+ double[] y = new double[N];
+
+ double k1 = 0;
+ double k2 = 0;
+ double k3 = 0;
+ double k4 = 0;
+ y[0] = y0;
+ for (int i = 1; i < 4; i++)
+ {
+ k1 = dt * f(t, y0);
+ k2 = dt * f(t + dt / 2, y0 + k1 / 2);
+ k3 = dt * f(t + dt / 2, y0 + k2 / 2);
+ k4 = dt * f(t + dt, y0 + k3);
+ y[i] = y0 + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
+ t += dt;
+ y0 = y[i];
+ }
+ for (int i = 4; i < N; i++)
+ {
+ y[i] = y[i - 1] + dt * (55 * f(t, y[i - 1]) - 59 * f(t - dt, y[i - 2]) + 37 * f(t - 2 * dt, y[i - 3]) - 9 * f(t - 3 * dt, y[i - 4])) / 24.0;
+ t += dt;
+ }
+ return y;
+ }
+ }
+}
\ No newline at end of file
diff --git a/src/Numerics/OdeSolvers/OdeSolvers.cs b/src/Numerics/OdeSolvers/RungeKutta.cs
similarity index 94%
rename from src/Numerics/OdeSolvers/OdeSolvers.cs
rename to src/Numerics/OdeSolvers/RungeKutta.cs
index dd3ab6fe..bbf82490 100644
--- a/src/Numerics/OdeSolvers/OdeSolvers.cs
+++ b/src/Numerics/OdeSolvers/RungeKutta.cs
@@ -43,7 +43,7 @@ namespace MathNet.Numerics.OdeSolvers
/// initial value
/// start time
/// end time
- /// Number of subintervals
+ /// Size of output array(the larger, the finer)
/// ode function
/// approximations
public static double[] SecondOrder(double y0, double start, double end, int N, Func f)
@@ -71,7 +71,7 @@ namespace MathNet.Numerics.OdeSolvers
/// initial value
/// start time
/// end time
- /// number of subintervals
+ /// Size of output array(the larger, the finer)
/// ode function
/// approximations
public static double[] FourthOrder(double y0, double start, double end, int N, Func f)
@@ -103,7 +103,7 @@ namespace MathNet.Numerics.OdeSolvers
/// initial vector
/// start time
/// end time
- /// number of subintervals
+ /// Size of output array(the larger, the finer)
/// ode function
/// approximations
public static Vector[] SecondOrder(Vector y0, double start, double end, int N, Func, Vector> f)
@@ -130,7 +130,7 @@ namespace MathNet.Numerics.OdeSolvers
/// initial vector
/// start time
/// end time
- /// number of subintervals
+ /// Size of output array(the larger, the finer)
/// ode function
/// approximations
public static Vector[] FourthOrder(Vector y0, double start, double end, int N, Func, Vector> f)
diff --git a/src/UnitTests/OdeSolvers/OdeSolverTest.cs b/src/UnitTests/OdeSolvers/OdeSolverTest.cs
index d8b3542b..265939a3 100644
--- a/src/UnitTests/OdeSolvers/OdeSolverTest.cs
+++ b/src/UnitTests/OdeSolvers/OdeSolverTest.cs
@@ -27,9 +27,9 @@
// OTHER DEALINGS IN THE SOFTWARE.
//
+using MathNet.Numerics.OdeSolvers;
using NUnit.Framework;
using System;
-using MathNet.Numerics.OdeSolvers;
using System.Linq;
namespace MathNet.Numerics.UnitTests.OdeSolvers
@@ -40,6 +40,90 @@ namespace MathNet.Numerics.UnitTests.OdeSolvers
[TestFixture, Category("OdeSolver")]
public class OdeSolverTest
{
+ [Test]
+ public void AB1Test()
+ {
+ Func ode = (t, y) => t + 2 * y * t;
+ Func sol = (t) => 0.5 * (Math.Exp(t * t) - 1);
+ double ratio = double.NaN;
+ double error = 0;
+ double oldError = 0;
+ for (int k = 0; k < 4; k++)
+ {
+ double y0 = 0;
+ double[] y_t = AdamsBashforth.FirstOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 8)), ode);
+ error = Math.Abs(sol(2) - y_t.Last());
+ if (oldError != 0)
+ ratio = Math.Log(oldError / error, 2);
+ oldError = error;
+ Console.WriteLine(string.Format("{0}, {1}", error, ratio));
+ }
+ Assert.AreEqual(1, ratio, 0.01);// Check error convergence order
+ }
+
+ [Test]
+ public void AB2Test()
+ {
+ Func ode = (t, y) => t + 2 * y * t;
+ Func sol = (t) => 0.5 * (Math.Exp(t * t) - 1);
+ double ratio = double.NaN;
+ double error = 0;
+ double oldError = 0;
+ for (int k = 0; k < 4; k++)
+ {
+ double y0 = 0;
+ double[] y_t = AdamsBashforth.SecondOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 8)), ode);
+ error = Math.Abs(sol(2) - y_t.Last());
+ if (oldError != 0)
+ ratio = Math.Log(oldError / error, 2);
+ oldError = error;
+ Console.WriteLine(string.Format("{0}, {1}", error, ratio));
+ }
+ Assert.AreEqual(2, ratio, 0.01);// Check error convergence order
+ }
+
+ [Test]
+ public void AB3Test()
+ {
+ Func ode = (t, y) => t + 2 * y * t;
+ Func sol = (t) => 0.5 * (Math.Exp(t * t) - 1);
+ double ratio = double.NaN;
+ double error = 0;
+ double oldError = 0;
+ for (int k = 0; k < 4; k++)
+ {
+ double y0 = 0;
+ double[] y_t = AdamsBashforth.ThirdOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 8)), ode);
+ error = Math.Abs(sol(2) - y_t.Last());
+ if (oldError != 0)
+ ratio = Math.Log(oldError / error, 2);
+ oldError = error;
+ Console.WriteLine(string.Format("{0}, {1}", error, ratio));
+ }
+ Assert.AreEqual(3, ratio, 0.01);// Check error convergence order
+ }
+
+ [Test]
+ public void AB4Test()
+ {
+ Func ode = (t, y) => t + 2 * y * t;
+ Func sol = (t) => 0.5 * (Math.Exp(t * t) - 1);
+ double ratio = double.NaN;
+ double error = 0;
+ double oldError = 0;
+ for (int k = 0; k < 4; k++)
+ {
+ double y0 = 0;
+ double[] y_t = AdamsBashforth.FourthOrder(y0, 0, 2, Convert.ToInt32(Math.Pow(2, k + 9)) + 1, ode);
+ error = Math.Abs(sol(2) - y_t.Last());
+ if (oldError != 0)
+ ratio = Math.Log(oldError / error, 2);
+ oldError = error;
+ Console.WriteLine(string.Format("{0}, {1}", error, ratio));
+ }
+ Assert.AreEqual(4, ratio, 0.01);// Check error convergence order
+ }
+
///
/// Runge-Kutta second order method for first order ODE.
///