unit Unit4;
{
  This software has been designed and is CopyLefted
  by Han de Bruijn:
                          (===)
                         @-O^O-@
                          #/_\#
                           ###
}
interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, ExtCtrls, Grafisch, Numeriek, Math;

type
  TForm1 = class(TForm)
    Image1: TImage;
    procedure Scheppen(Sender: TObject);
    procedure Toetsdruk(Sender: TObject; var Key: Char);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

const
  N : integer = 20;
  p : double = 5;
var
  FEM : Numerical;

procedure Rekenen;
{
  Calculations
}
var
  i : integer;
  dx : double;
begin
  SetLength(FEM.nr,2);
  for i := 1 to N-1 do
  begin
    FEM.nr[0] := i; FEM.nr[1] := i+1;
    FEM.Layout;
  end;
  Writeln('Matrix size = ',FEM.nn,' x ',FEM.nb1);
  FEM.Globaal_nul;
  FEM.Element_nul(2);
  dx := 1/(N-1);
  FEM.e[0][0] := 1/dx + sqr(p)/3*dx;
  FEM.e[1][1] := FEM.e[0][0];
  FEM.e[0][1] := -1/dx + sqr(p)/6*dx;
  FEM.e[1][0] := FEM.e[0][1]; 
  FEM.r[0] := 0; FEM.r[1] := 0;
  for i := 1 to N-1 do
  begin
    FEM.nr[0] := i; FEM.nr[1] := i+1;
    FEM.Intellen; { Assembly }
  end;
  FEM.E[0][0] := 1; FEM.r[0] := 1;
  FEM.nr[0] := 1;
  FEM.Randvoorwaarde; { b.c. }
  FEM.Oplossen; { Solver }
end;

procedure Tekenen;
{
  Graphics
  and Print
}
var
  i,j,k : integer;
  exact : double;
begin
  Form1.Image1.Canvas.Pen.Width := 2;
  Form1.Image1.Canvas.Pen.Color := clBlack;
  Form1.Image1.Canvas.Brush.Color := clBlack;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(0));
  Form1.Image1.Canvas.LineTo(x2i(1),y2j(0));
  for k := 0 to N-1 do
  begin
    i := x2i(k/(N-1)); j := y2j(0);
    Form1.Image1.Canvas.Ellipse(i-4,j-4,i+4,j+4);
  end;
  Form1.Image1.Canvas.Pen.Color := clGreen;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(1));
  for k := 0 to N-1 do
  begin
    exact := cosh(p*(1-k/(N-1)))/cosh(p);
    i := x2i(k/(N-1)); j := y2j(exact);
    Form1.Image1.Canvas.LineTo(i,j);
    Writeln(FEM.b[k],' =',exact);
  end;
  Form1.Image1.Canvas.Pen.Color := clRed;
  Form1.Image1.Canvas.MoveTo(x2i(0),y2j(1));
  for k := 1 to N-1 do
  begin
    i := x2i(k/(N-1)); j := y2j(FEM.b[k]);
    Form1.Image1.Canvas.LineTo(i,j);
  end;
end;

procedure TForm1.Scheppen(Sender: TObject);
{
  On Create
}
begin
  Rekenen;
  TV(Form1.Image1);
  ClearDevice;
  xmin := -0.01; xmax := 1.01;
  ymin := -0.01; ymax := 1.01;
  Tekenen;
end;

procedure TForm1.Toetsdruk(Sender: TObject; var Key: Char);
{
  On KeyPress
}
begin
  Exit;
end;

end.