using System;

using System.Collections.Generic;

using System.Linq;

public class Program

{

    public static void Main()

    {

        var points = SweepingMethod(0.01);

        foreach (var point in points) {

            Console.WriteLine("({0:0.000};  {1})", point.X, point.Y);   

        }   

    }

    public static List<Point> SweepingMethod(double step)

    {

        var mus = new List<double> { 0.0 };

        var lambdas = new List<double> { 0.0 };

        var x = 0.0;

​

        //lambdas.Add(2.0 / (2.0 + step * step));

        //mus.Add((-1.0) * (Q(x) * step * step - 96.0 * step) / (2.0 + step * step));

​

        lambdas.Add(12.0);

        mus.Add(12.0 * step);

​

        //var y_1 = OriginalFunction(0.01);

        //var d_y_0 = lambdas.Last() * y_1 + mus.Last();

        //var y_0 = OriginalFunction(0.0);

​

        while (x + step < 1 - Tolerance)

        {

            x += step;

            var l = -1.0 / (-2.0 - step * step + lambdas.Last());

            var m = (Q(x) * step * step - mus.Last()) / (lambdas.Last() - 2.0 - step * step);

            lambdas.Add(l);

            mus.Add(m);

        }

​

        var mu = mus.Last();

        var lambda = lambdas.Last();

​

//        var y = (Q(1.0) * step * step - 2.0 * step * (2.0 * Math.Exp(1) + 46.0) - 2.0 * mu) / (2.0 * lambda - 2.0 - 2.0 * step - step * step);

        var y = (-step*(Math.Exp(1.0) - 1.0/(Math.Exp(1.0)) + 12.0)) / (lambda - 1.0);

        var ys = new List<double> { y };

​

        for (var i = lambdas.Count - 1; i > 0; i--)

        {

            y = lambdas[i] * ys.Last() + mus[i];

            ys.Add(y);

        }

        ys.Reverse();

​

        return ys.Select((element, index) => new Point(index * step, element)).ToList();

    }

​

    private static double Q(double x)

    {

        return 12.0 * x * (1.0 - x) + 26.0;

        //return 36.0 * x * (1.0 - x) + 74.0;

        //return 48.0 * x * (1.0 - x) + 98.0;

    }

    private const double Tolerance = 0.000001;

}

​

public class Point

{

    public double X { get; set; }

    public double Y { get; set; }

​

    public Point(double x, double y)

    {

        X = x;

        Y = y;

    }

}