Пример решения уравнения

с помощью метода Рунге-Кутты:

using System;

using System.Collections.Generic;

using System.ComponentModel;

using System.Data;

using System.Drawing;

using System.IO;

using System.Drawing.Drawing2D;

using System.Linq;

using System.Text;

using System.Windows.Forms;

namespace WindowsFormsApplication3

{

public partial class Form1: Form

{

double[] t, y, y1; int n=50;double dt=0.01,T0=0,Y0=0;

int i = 0; Double My = 0, MaxY = 0,Mt=0,MaxT=0,My1=0,MaxY1=0;

Bitmap myBmp,myBmp2;

public Form1()

{

InitializeComponent();

}

private void button1_Click(object sender, EventArgs e)

{ //Решение

dataGridView1.Rows.Clear();

t = new double[n+1];

y = new double[n + 1];

y1 = new double[n + 1];

T0 = Convert.ToDouble(textBox1.Text);

Y0 = Convert.ToDouble(textBox2.Text);

dt = Convert.ToDouble(textBox3.Text);

t[0]=T0;

y[0]=Y0;

y1[0]=dYdt(t[0],y[0]);

for (i = 1; i < n + 1; i++)

{

t[i] =T0+ dt * i;

y[i]=y[i-1]+Dy(t[i-1],y1[i-1]);

y1[i]=dYdt(t[i],y[i]);

}

for (i = 0; i < n+1; i++)

{

// Заполнение таблицы

dataGridView1.Rows.Add();

dataGridView1.Rows[i].Cells[0].Value = i;

dataGridView1.Rows[i].Cells[1].Value = t[i];

dataGridView1.Rows[i].Cells[2].Value = y[i];

dataGridView1.Rows[i].Cells[3].Value = y1[i];

}

if (checkBox1.Checked)

{

postroenie();

}

}

double dYdt(double D,double S)

{

//Выражение для производной

return 9*Math.Cos(Math.PI*D) * Math.Exp(-D)-S;

}

private void button2_Click(object sender, EventArgs e)

{

Close();

}

double Dy(double D,double S)

{

//Коэффициенты метода Рунге-Кутты

double K1, K2, K3, K4;

K1=dt*dYdt(t[i-1],y[i-1]);

K2 = dt * dYdt(t[i - 1]+dt/2, y[i - 1]+K1/2);

K3 = dt * dYdt(t[i - 1] + dt / 2, y[i - 1] + K2 / 2);

K4 = dt * dYdt(t[i - 1]+dt, y[i - 1]+K3);

return 1.0/6*(K1+2*K2+2*K3+K4);

}

void postroenie()

{

// Построение графика

int[] yint, y1int, tint;

if (t== null || y==null ||y1 ==null) return;

MaxY = 0;

MaxY1 = 0;

MaxT = 0;

myBmp = new Bitmap(pictureBox1.Width, pictureBox1.Height);

Graphics gr1 = Graphics.FromImage(myBmp);

Pen P1 = new Pen(Color.Red, 2);

gr1.DrawRectangle(P1, 1, 1, pictureBox1.Width - 2, pictureBox1.Height - 2);

for (int i = 0; i < n+1; i++)

{

if (System.Math.Abs(y[i]) > MaxY)

{

MaxY = System.Math.Abs(y[i]);;

}

if (System.Math.Abs(t[i]) > MaxT)

{

MaxT = System.Math.Abs(t[i]);

}

if (System.Math.Abs(y1[i]) > MaxY1)

{

MaxY1 = System.Math.Abs(y1[i]);

}

}

My = (pictureBox1.Height) / 2.2 / MaxY;

My1 = (pictureBox1.Height) / 2.2 / MaxY1;

Mt = (pictureBox1.Width) / 2.2 / MaxT;

yint = new int[n + 1];

y1int = new int[n + 1];

tint = new int[n + 1];

for (int i = 0; i < n+1; i++)

{

yint[i] = (pictureBox1.Height) / 2 -Convert.ToInt32(y[i] * My);

y1int[i] = (pictureBox1.Height) / 2-Convert.ToInt32(y1[i] * My1);

tint[i] = pictureBox1.Width/2+Convert.ToInt32(t[i] * Mt);

}

Pen P2 = new Pen(Color.Green, 6);

for (int i = 0; i < n; i++)

{

gr1.DrawLine(P2, tint[i], yint[i],tint[i+1],yint[i+1]);

}

Pen P3 = new Pen(Color.Brown, 6);

for (int i = 0; i < n; i++)

{

gr1.DrawLine(P3, tint[i], y1int[i], tint[i + 1], y1int[i + 1]);

}

Pen P4 = new Pen(Color.Black, 3);

//Стиль линии с наконечниками

P4.SetLineCap(LineCap.Flat, LineCap.ArrowAnchor, DashCap.Flat);

//Кисть для шрифта на рисунке

Brush B2 = new SolidBrush(Color.Black);

System.Drawing.Font E = new Font("time new roman", 14);

// Вывод надписей на рисунке

gr1.DrawString("y dy/dt", E, B2, pictureBox1.Width / 2-20,0);

gr1.DrawString("t", E, B2, pictureBox1.Width-20,pictureBox1.Height / 2);

gr1.DrawLine(P4, 10, (pictureBox1.Height) / 2, pictureBox1.Width - 10, (pictureBox1.Height) / 2);

gr1.DrawLine(P4, pictureBox1.Width/2, (pictureBox1.Height) -10,pictureBox1.Width/2, 10);

pictureBox1.Image = myBmp;

legenda();

}

void legenda()

{// Вывод легенды

myBmp2 = new Bitmap(pictureBox2.Width, pictureBox2.Height);

Graphics gr1 = Graphics.FromImage(myBmp2);

Pen P1 = new Pen(Color.Green, 6);

gr1.DrawLine(P1, pictureBox2.Width / 2, 20, pictureBox2.Width -10,20);

Pen P2 = new Pen(Color.Brown, 6);

gr1.DrawLine(P2, pictureBox2.Width / 2, 50, pictureBox2.Width - 10, 50);

Brush B2 = new SolidBrush(Color.Black);

System.Drawing.Font E = new Font("time new roman", 14);

gr1.DrawString("y(t)", E, B2, 7, 7);

gr1.DrawString("dy/dt", E, B2, 7, 37);

pictureBox2.Image = myBmp2;

}

}

}

Рис. 6.1 Форма проекта.