mathnet-numerics/src/UnitTests/OdeSolvers/OdeSolverTest.cs

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using MathNet.Numerics.OdeSolvers;
using NUnit.Framework;
using System;
using System.Linq;

namespace MathNet.Numerics.UnitTests.OdeSolvers
{
    /// <summary>
    /// ODE Solver tests.
    /// </summary>
    [TestFixture, Category("OdeSolver")]
    public class OdeSolverTest
    {
        [Test]
        public void AB1Test()
        {
            Func<double, double, double> ode = (t, y) => t + 2 * y * t;
            Func<double, double> 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<double, double, double> ode = (t, y) => t + 2 * y * t;
            Func<double, double> 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<double, double, double> ode = (t, y) => t + 2 * y * t;
            Func<double, double> 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<double, double, double> ode = (t, y) => t + 2 * y * t;
            Func<double, double> 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
        }

        /// <summary>
        /// Runge-Kutta second order method for first order ODE.
        /// </summary>
        [Test]
        public void RK2Test()
        {
            Func<double, double, double> ode = (t, y) => t + 2 * y * t;
            Func<double, double> 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 = RungeKutta.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);
                oldError = error;
                //Console.WriteLine(string.Format("{0}, {1}", error, ratio));
            }
            Assert.AreEqual(2, ratio, 0.01);// Check error convergence order
        }

        /// <summary>
        /// Runge-Kutta fourth order method for first order ODE.
        /// </summary>
        [Test]
        public void RK4Test()
        {
            Func<double, double, double> ode = (t, y) => t + 2 * y * t;
            Func<double, double> 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 = RungeKutta.FourthOrder(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);
                oldError = error;
                //Console.WriteLine(string.Format("{0}, {1}", error, ratio));
            }
            Assert.AreEqual(4, ratio, 0.01);// Check error convergence order
        }
    }
}