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@ -55,6 +55,7 @@ namespace MathNet.Numerics.OdeSolvers |
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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(Require two initial guesses)
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/// </summary>
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@ -64,23 +65,22 @@ namespace MathNet.Numerics.OdeSolvers |
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/// <param name="N">Number of subintervals</param>
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/// <param name="f">ode model</param>
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/// <returns></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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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 fold = f(t, y0); |
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double ytilde = y0 + (2*dt/3) * fold; |
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double y1 = y0 + (dt/4) * fold + (3*dt/4) * f(t + (2*dt/3), ytilde ); |
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double fold = f(t, y0); |
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double ytilde = y0 + 2.0 * dt / 3.0 * fold; |
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double y1 = y0 + dt / 4.0 * fold + 3.0 * dt / 4 * f(t + 2.0 / 3.0 * dt, ytilde); |
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y[0] = y0; |
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t += dt; |
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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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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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