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| using System;
using System.Collections.Generic;
using System.Windows.Forms;
using System.IO;
namespace lab11
{
public partial class Form1 : Form
{
static double h;
static double e0;
static double a, b;
static double[] x, y, y1;
public Form1()
{
InitializeComponent();
}
private void Button1_Click(object sender, EventArgs e)
{
label6.Text = "";
chart1.Series[0].Points.Clear();
chart1.Series[1].Points.Clear();
chart1.Series[2].Points.Clear();
chart1.Series[3].Points.Clear();
a = Double.Parse(textBox1.Text);
b = Double.Parse(textBox2.Text);
string path = "1.txt";
StreamWriter w = new StreamWriter(path);
if (radioButton1.Checked)
{
h = Double.Parse(textBox3.Text);
int L = (int)((b - a) / h) + 1;
x = new double[L];
y = new double[L];
y[0] = Double.Parse(textBox5.Text);
for (int i = 0; i < L; i++)
x[i] = a + i * h;
if (textBox6.Text == "")
{
double[] RealY = new double[L];
for (int i = 0; i < L; i++)
{
RealY[i] = Math.Pow(x[i], 3) + x[i];
}
for (int i = 1; i < L; i++)
{
double k1, k2, k3, k4;
k1 = h * function1(x[i - 1], y[i - 1]);
k2 = h * function1(x[i - 1] + h / 2, y[i - 1] + k1 / 2);
k3 = h * function1(x[i - 1] + h / 2, y[i - 1] + k2 / 2);
k4 = h * function1(x[i - 1] + h, y[i - 1] + k3);
y[i] = y[i - 1] + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
}
for (int i = 0; i < L; i++)
{
chart1.Series[0].Points.AddXY(x[i], y[i]);
}
double norm = 0;
for (int i = 0; i < L; i++)
{
if (norm < Math.Abs(y[i] - RealY[i]))
norm = Math.Abs(y[i] - RealY[i]);
}
}
else
{
y1 = new double[L];
y1[0] = Double.Parse(textBox6.Text);
for (int i = 1; i < L; i++)
{
double k1, k2, k3, k4;
double q1, q2, q3, q4;
k1 = h * function2(x[i - 1], y[i - 1], y1[i - 1]);
q1 = h * function3(x[i - 1], y[i - 1], y1[i - 1]);
k2 = h * function2(x[i - 1], y[i - 1] + k1 / 2, y1[i - 1] + q1 / 2);
q2 = h * function3(x[i - 1], y[i - 1] + k1 / 2, y1[i - 1] + q1 / 2);
k3 = h * function2(x[i - 1], y[i - 1] + k1 / 2, y1[i - 1] + q2 / 2);
q3 = h * function3(x[i - 1], y[i - 1] + k1 / 2, y1[i - 1] + q2 / 2);
k4 = h * function2(x[i - 1], y[i - 1] + k3, y1[i - 1] + q3);
q4 = h * function3(x[i - 1], y[i - 1] + k3, y1[i - 1] + q3);
y[i] = y[i - 1] + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
y1[i] = y1[i - 1] + (q1 + 2 * q2 + 2 * q3 + q4) / 6;
}
double[] RealY = new double[L];
double[] RealY1 = new double[L];
for (int i = 0; i < L; i++)
{
RealY[i] = Math.Cos(x[i]);
RealY1[i] = Math.Sin(x[i]);
}
double norm = 0;
for (int i = 0; i < L; i++)
{
if (norm < Math.Abs(y[i] - RealY[i]))
norm = Math.Abs(y[i] - RealY[i]);
if (norm < Math.Abs(y1[i] - RealY1[i]))
norm = Math.Abs(y1[i] - RealY1[i]);
}
label6.Text = norm.ToString();
w.WriteLine("X Y Y1 RealY RealY1");
for (int i = 0; i < L; i++)
{
chart1.Series[0].Points.AddXY(x[i], y[i]);
chart1.Series[1].Points.AddXY(x[i], y1[i]);
chart1.Series[2].Points.AddXY(x[i], RealY[i]);
chart1.Series[3].Points.AddXY(x[i], RealY1[i]);
w.WriteLine(x[i].ToString("0.000000") + "\t" + y[i].ToString("0.000000") + "\t" + y1[i].ToString("0.000000") + "\t" + RealY[i].ToString("0.000000") + "\t" + RealY1[i].ToString("0.000000"));
}
}
}
else
{
double X = a;
double Y = Double.Parse(textBox5.Text);
double Y1 = Double.Parse(textBox6.Text);
e0 = Double.Parse(textBox4.Text);
List<double> Xlist = new List<double>();
List<double> Ylist = new List<double>();
List<double> Y1list = new List<double>();
double k1, k2, k3, k4;
double q1, q2, q3, q4;
while (X<=b)
{
Xlist.Add(X);
Ylist.Add(Y);
Y1list.Add(Y1);
if (X == b) break;
h = CalcH(X,Y,Y1);
k1 = h * function2(X, Y, Y1);
q1 = h * function3(X, Y, Y1);
k2 = h * function2(X + h / 2, Y + k1 / 2, Y1 + q1 / 2);
q2 = h * function3(X + h / 2, Y + k1 / 2, Y1 + q1 / 2);
k3 = h * function2(X + h / 2, Y + k2 / 2, Y1 + q2 / 2);
q3 = h * function3(X + h / 2, Y + k2 / 2, Y1 + q2 / 2);
k4 = h * function2(X + h, Y + k3, Y1 + q3);
q4 = h * function3(X + h, Y + k3, Y1 + q3);
Y += (k1 + 2 * k2 + 2 * k3 + k4) / 6;
Y1 += (q1 + 2 * q2 + 2 * q3 + q4) / 6;
if (X + h > b)
X = b;
else X += h;
}
double[] RealY = new double[Ylist.Count];
double[] RealY1 = new double[Ylist.Count];
for (int i = 0; i < Ylist.Count; i++)
{
RealY[i] = Math.Cos(Xlist[i]);
RealY1[i] = Math.Sin(Xlist[i]);
}
double norm = 0;
for (int i = 0; i < Ylist.Count; i++)
{
if (norm < Math.Abs(Ylist[i] - RealY[i]))
norm = Math.Abs(Ylist[i] - RealY[i]);
if (norm < Math.Abs(Y1list[i] - RealY1[i]))
norm = Math.Abs(Y1list[i] - RealY1[i]);
}
label6.Text = norm.ToString();
w.WriteLine("X Y Y1 RealY RealY1");
for (int i = 0; i < Ylist.Count; i++)
{
chart1.Series[0].Points.AddXY(Xlist[i], Ylist[i]);
chart1.Series[1].Points.AddXY(Xlist[i], Y1list[i]);
chart1.Series[2].Points.AddXY(Xlist[i], RealY[i]);
chart1.Series[3].Points.AddXY(Xlist[i], RealY1[i]);
w.WriteLine(Xlist[i].ToString("0.000000") + "\t" + Ylist[i].ToString("0.000000") + "\t" + Y1list[i].ToString("0.000000") + "\t" + RealY[i].ToString("0.000000") + "\t" + RealY1[i].ToString("0.000000"));
}
}
w.Close();
}
public double function2(double x, double y1, double y2)
{
return -y2;
}
public double function3(double x, double y1, double y2)
{
return y1;
}
public double function1(double x, double y)
{
return -30 * y;
}
public double CalcH(double x, double y, double y1)
{
int count = 0;
double h = Math.Abs(x-b);
double E,E1,E2;
double k1, k2, k3, k4;
double q1, q2, q3, q4;
while (count < 10000)
{
k1 = h * function2(x, y, y1);
q1 = h * function3(x, y, y1);
k2 = h * function2(x + h / 2, y + k1 / 2, y1 + q1 / 2);
q2 = h * function3(x + h / 2, y + k1 / 2, y1 + q1 / 2);
k3 = h * function2(x + h / 2, y + k2 / 2, y1 + q2 / 2);
q3 = h * function3(x + h / 2, y + k2 / 2, y1 + q2 / 2);
k4 = h * function2(x + h, y + k3, y1 + q3);
q4 = h * function3(x + h, y + k3, y1 + q3);
E1 = Math.Abs(2 * (k1 - k2 - k3 + k4) / 3);
E2 = Math.Abs(2 * (q1 - q2 - q3 + q4) / 3);
if (E1 < E2)
E = E2;
else E = E1;
if (E > e0)
h /= 2;
else break;
count++;
}
return h;
}
}
} |
(
