// <copyright file="AdamsBashforth.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2016 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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namespace IStation.Numerics.OdeSolvers
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{
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public static class AdamsBashforth
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{
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/// <summary>
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/// First Order AB method(same as Forward Euler)
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/// </summary>
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/// <param name="y0">Initial value</param>
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/// <param name="start">Start Time</param>
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/// <param name="end">End Time</param>
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/// <param name="N">Size of output array(the larger, the finer)</param>
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/// <param name="f">ode model</param>
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/// <returns>approximation with size N</returns>
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public static double[] FirstOrder(double y0, double start, double end, int N, Func<double, double, double> f)
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{
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double dt = (end - start) / (N - 1);
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double t = start;
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double[] y = new double[N];
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y[0] = y0;
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for (int i = 1; i < N; i++)
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{
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y[i] = y0 + dt * f(t, y0);
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t += dt;
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y0 = y[i];
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}
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return y;
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}
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/// <summary>
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/// Second Order AB Method
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/// </summary>
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/// <param name="y0">Initial value 1</param>
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/// <param name="start">Start Time</param>
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/// <param name="end">End Time</param>
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/// <param name="N">Size of output array(the larger, the finer)</param>
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/// <param name="f">ode model</param>
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/// <returns>approximation with size N</returns>
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public static double[] SecondOrder(double y0, double start, double end, int N, Func<double, double, double> f)
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{
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double dt = (end - start) / (N - 1);
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double t = start;
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double[] y = new double[N];
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double k1 = f(t, y0);
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double k2 = f(t + dt, y0 + dt * k1);
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double y1 = y0 + 0.5 * dt * (k1 + k2);
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y[0] = y0;
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y[1] = y1;
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for (int i = 2; i < N; i++)
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{
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y[i] = y1 + dt * (1.5 * f(t + dt, y1) - 0.5 * f(t, y0));
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t += dt;
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y0 = y[i - 1];
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y1 = y[i];
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}
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return y;
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}
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/// <summary>
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/// Third Order AB Method
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/// </summary>
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/// <param name="y0">Initial value 1</param>
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/// <param name="start">Start Time</param>
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/// <param name="end">End Time</param>
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/// <param name="N">Size of output array(the larger, the finer)</param>
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/// <param name="f">ode model</param>
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/// <returns>approximation with size N</returns>
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public static double[] ThirdOrder(double y0, double start, double end, int N, Func<double, double, double> f)
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{
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double dt = (end - start) / (N - 1);
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double t = start;
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double[] y = new double[N];
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double k1 = 0;
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double k2 = 0;
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double k3 = 0;
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double k4 = 0;
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y[0] = y0;
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for (int i = 1; i < 3; i++)
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{
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k1 = dt * f(t, y0);
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k2 = dt * f(t + dt / 2, y0 + k1 / 2);
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k3 = dt * f(t + dt / 2, y0 + k2 / 2);
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k4 = dt * f(t + dt, y0 + k3);
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y[i] = y0 + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
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t += dt;
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y0 = y[i];
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}
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for (int i = 3; i < N; i++)
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{
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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;
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t += dt;
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}
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return y;
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}
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/// <summary>
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/// Fourth Order AB Method
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/// </summary>
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/// <param name="y0">Initial value 1</param>
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/// <param name="start">Start Time</param>
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/// <param name="end">End Time</param>
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/// <param name="N">Size of output array(the larger, the finer)</param>
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/// <param name="f">ode model</param>
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/// <returns>approximation with size N</returns>
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public static double[] FourthOrder(double y0, double start, double end, int N, Func<double, double, double> f)
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{
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double dt = (end - start) / (N - 1);
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double t = start;
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double[] y = new double[N];
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double k1 = 0;
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double k2 = 0;
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double k3 = 0;
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double k4 = 0;
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y[0] = y0;
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for (int i = 1; i < 4; i++)
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{
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k1 = dt * f(t, y0);
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k2 = dt * f(t + dt / 2, y0 + k1 / 2);
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k3 = dt * f(t + dt / 2, y0 + k2 / 2);
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k4 = dt * f(t + dt, y0 + k3);
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y[i] = y0 + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
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t += dt;
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y0 = y[i];
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}
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for (int i = 4; i < N; i++)
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{
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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;
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t += dt;
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}
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return y;
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}
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}
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}
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