Практическая часть. 
Анализ и сравнение численных методов решения нелинейных уравнений

unit Unit1;

interface.

uses.

Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,.

Dialogs, ExtCtrls, TeeProcs, TeEngine, Chart, StdCtrls, Series;

type.

TForm1 = class (TForm).

Label3: TLabel;

Button1: TButton;

Edit3: TEdit;

Edit4: TEdit;

Chart1: TChart;

Series1: TFastLineSeries;

Edit2: TEdit;

Edit5: TEdit;

Button3: TButton;

Label2: TLabel;

Button2: TButton;

Label4: TLabel;

Button4: TButton;

Button5: TButton;

Panel1: TPanel;

Panel2: TPanel;

Edit6: TEdit;

Label5: TLabel;

Panel3: TPanel;

Edit9: TEdit;

Label8: TLabel;

Button6: TButton;

Button7: TButton;

Button8: TButton;

Button9: TButton;

Label6: TLabel;

Label7: TLabel;

Label1: TLabel;

procedure Button1Click (Sender: TObject);

procedure Button3Click (Sender: TObject);

procedure Button2Click (Sender: TObject);

procedure Button4Click (Sender: TObject);

procedure Button5Click (Sender: TObject);

procedure Button6Click (Sender: TObject);

procedure Button7Click (Sender: TObject);

procedure Button8Click (Sender: TObject);

procedure Button9Click (Sender: TObject);

// procedure Label3Click (Sender: TObject);

private.

{ Private declarations }.

public.

{ Public declarations }.

end;

var.

Form1: TForm1;

implementation.

uses Unit2;

{$R *.dfm}.

function F (x:real): real;

begin.

result:=2*cos ((x+pi/6))+x*x-4*x+3;

end;

function F1(x:real): real;

begin.

result:=2*(x-1/6*(6*x+pi)*sin (x)+cos (x)-2);

end;

procedure TForm1. Button1Click (Sender: TObject);

Var a, y, x0,y1,b, x1, xn, xn1: real;

x, e, Fx, Fx1: real;

begin.

e:=strtofloat (edit3.Text);

a:=StrToFloat (Edit2.Text);

b:=StrToFloat (Edit5.Text);

x0:=a;

x:=x0-f (x0)/f1(x0);

repeat.

begin.

x1:=x;

y:=f (x);

y1:=f1(x);

x:=x-y/y1;

end;

until (x-x1)>e;

Repeat.

x:=x-(F (x)/F1(x));

Until abs (f (x)).

edit4.Text:=FloatToStr (x);

end;

procedure TForm1. Button3Click (Sender: TObject);

var.

a, b, h: real;

i, n: integer;

begin.

a:=StrToFloat (Form1.Edit2.Text);

b:=StrToFloat (Form1.Edit5.Text);

n:=100;

h:=(b-a)/n;

Form1.Series1.AddXY (a, f (a));

for i:=1 to n do.

Form1.Series1.AddXY (a+h*i, f (a+h*i));

end;

procedure TForm1. Button2Click (Sender: TObject);

begin.

Form1.Series1.Clear;

end;

procedure TForm1. Button4Click (Sender: TObject);

var x, c, a, b, e:real;

begin.

e:=strtofloat (Edit6.Text);

a:=strtofloat (edit2.Text);

b:=strtofloat (edit5.Text);

repeat.

c:=(a+b)/2;

if f (a)*f (c)<0 then b:=c else a:=c;

until b-a.

x:=(a+b)/2;

begin.

edit4.Text:=FloatToStr (x);

end;

end;

procedure TForm1. Button5Click (Sender: TObject);

Var a, b, c, g, e, x, x0,x1,y:real;

Fx: real;

begin.

e:=strtofloat (edit9.text);

a:=strtofloat (edit2.Text);

b:=strtofloat (edit5.Text);

c:=a;

repeat.

g:=c;

c:=(a*f (b)-b*f (a))/(f (b)-f (a));

if f (a)*f (c)<0 then b:=c else a:=c;

until abs (c-g).

Form1.Edit4.Text:=(floattostr (c));

end;

procedure TForm1. Button6Click (Sender: TObject);

begin.

panel1.Visible:=true;

panel2.Visible:=false;

panel3.Visible:=false;

end;

procedure TForm1. Button7Click (Sender: TObject);

begin.

panel2.Visible:=true;

panel1.Visible:=false;

panel3.Visible:=false;

end;

procedure TForm1. Button8Click (Sender: TObject);

begin.

panel3.Visible:=true;

panel1.Visible:=false;

panel2.Visible:=false;

end;

procedure TForm1. Button9Click (Sender: TObject);

begin.

form2.showmodal;

end;

end.

Метод половинного деления.
Точность.	0,001.
Интервал.	(-1,2).
Ответ.	1,2 404.

Метод хорд.
Точность.	0,001.
Интервал.	(-1,2).
Ответ.	1,2 383.