{==================}Program Runge_Kutt_Diff_Ur;{======================}
     {Ðåøåíèå äèôôåðåíöèàëüíûõ óðàâíåíèé ìåòîäàìè Ðóíãå-Êóòòà}
     {Ëàáîðàòîðíàÿ ðàáîòà ïî âû÷èñëèòåëüíîé ôèçèêå (×ÌèÌÌ) ¹2}
(*^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^*)
 {[][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][][]}
(*<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>*)
{
                Û²°                        2002ã.  v4.0   (December, 1)                                      Îêðóãèí Àëåêñàíäð
                 =    Âàðèàíò 2;      çàäàíèå 4/2
   ~~~~~~~      +++    ~~~~~~~       /-_-_-_-_-^^^-_-_!_-_-^^^-_-_-_-_-\
    ~~~~~      !!!!!    ~~~~~        |ÛÛÛÛÛÛÛÛÛÛÛ\ÛÛÛÛÛÛÛÛÛ/ÛÛÛÛÛÛÛÛÛÛÛ|
     ~~~      _______    ~~~         |Û/\²²²²²²²²²²\²²^²²/²²²²²²²²²²/\Û|
      ~      ---------    ~          |ÛÛ\\²²°°°°°°°°°\°/°°°°°°°°°²²//ÛÛ|
            ###########              |ÛÛÛ²\²°°°ÚÄÄÄÄÄÄ|ÄÄÄÄÄÄ¿°°°²/²ÛÛÛ|
    |||    ^^^^^^^^^^^^^    |||      |ÛÛÛ²²\°°°³ÉÍÍÍÍÍþÍÍÍÍÍ»³°°°/²²ÛÛÛ|
    |||   ÉÍÍÍÍÍÍÍÍÍÍÍÍÍ»   |||      |Û*Û²²²\°°³ºßß!ßßßßß!ßߺ³°°/²²²Û*Û|
    |||  |ºÚÄÄÄÄÄÄÄÄÄÄÄ¿º|  |||      |ÛÛÛ²²²°\°³ºÝÞÝÞÝÜÝÞÝÞݺ³°/°²²²ÛÛÛ|
        Þ|º³ÛÛÛÛÛÛÛÛÛÛÛ³º|Ý          |ÛÛÛ²²²°°\³ºÞÝÞÝÞßÞÝÞÝÞº³/°°²²²ÛÛÛ|
  ßßßß þÞ|º³Û²²²²²²²²²Û³º|Ýþ ÜÜÜÜ    |ÛÛ<>²<>°#-þßÜßÜßXßÜßÜßþ-#°<>²<>ÛÛ|
   <<< þÞ|º³Û²²°°°°°²²Û³º|Ýþ >>>     |ÛÛÛ²²²°°/³ºÞÝÞÝÞßÞÝÞÝÞº³\°°²²²ÛÛÛ|
  ßßßß þÞ|º³Û²²°°*°°²²Û³º|Ýþ ÜÜÜÜ    |ÛÛÛ²²²°/°³ºÝÞÝÞÝÜÝÞÝÞݺ³°\°²²²ÛÛÛ|
   >>> þÞ|º³Û²²°°°°°²²Û³º|Ýþ <<<     |Û*Û²²²/°°³ºÜ!ÜÜÜÜÜÜÜ!ܺ³°°\²²²Û*Û|
  ßßßß þÞ|º³Û²²²²²²²²²Û³º|Ýþ ÜÜÜÜ    |ÛÛÛ²²/°°°³ÈÍÍÍÍÍþÍÍÍÍͼ³°°°\²²ÛÛÛ|
        Þ|º³ÛÛÛÛÛÛÛÛÛÛÛ³º|Ý          |ÛÛÛ²/²°°°ÀÄÄÄÄÄÄ|ÄÄÄÄÄÄÙ°°°²\²ÛÛÛ|
   ///   |ºÀÄÄÄÄÄÄÄÄÄÄÄÙº|  \\\      |ÛÛ//²²°°°°°°°°°/°\°°°°°°°°°²²\\ÛÛ|
          ÈÍÍÍÍÍÍÍÍÍÍÍÍͼ            |Û\/²²²²²²²²²²/²²#²²\²²²²²²²²²²\/Û|
  /ÛÛÛÛÛÛÛÛÛßßßßßßßßßßßÛÛÛÛÛÛÛÛÛ\    |ÛÛÛÛÛÛÛÛÛÛÛ/ÛÛÛÛÛÛÛÛÛ\ÛÛÛÛÛÛÛÛÛÛÛ|
  \ÛÛÛÛÛÛÛÛÛÜÜÜÜÜÜÜÜÜÜÜÛÛÛÛÛÛÛÛÛ/    \-+-+-+-+-<<<-+-+=+-+->>>-+-+-+-+-/
}
{$N+}
{$D-}
Uses Graph, CRT;
const
  t0  :  Extended = 0.0  ;
  x0  :  Extended = 10.0 ;
  b   :  Extended = 6.0 ;
  h0  :  Extended = 0.5 ;
  ScaleX  :  Extended = 0.53 ;
  ScaleT  :  Extended = 100.0 ;
var
  D, R, e : Integer;
  i : Integer;
  N : Byte;
  x, t, h, C, C1, C2, C3, C4 : Extended;
  delta, tt : Extended;
  {   ^   }
  xk {x}, x1, k1, k2, k3, k4, S, eps {epsilon} : Extended;
  SSS : String;
{-=-=-=-=-=-=-=-=-=-=-=-=-}
Function f(t, x : Extended) : Extended;{Èíòåãðèðóåìàÿ ôóíêöèÿ}
begin
 f:= -2*(t-2.0)*x + Exp(-t*t+4.0*t)*(2.0*t+1.0);
end;
{_+_+_+_+_+_+_+_+_+_+_+_+_+_+_}
Function ff(t : Extended) : Extended;{Àíàëèòè÷åñêîå ðåøåíèå}
begin
 ff:= (t*(t+1.0)+10.0)*exp(-t*(t-4.0));
end;
{[][][[][[][][][][][][][][]}
Procedure View(tr, Anr, RKr : Extended);
begin
  Str(tr:5:5, SSS);
  OutTextXY(350, 10+N*14, SSS);
  Str(Anr:5:5, SSS);
  OutTextXY(430, 10+N*14, SSS);
  Str(RKr:5:5, SSS);
  OutTextXY(540, 10+N*14, SSS)
end;
{-----------------------}
Procedure DoScreen;
begin
  ClearViewPort;
  SetColor(DarkGray);
  MoveTo(0, 477);
  LineTo(640, 477);
  LineTo(630, 475);
  LineTo(630, 479);
  LineTo(640, 477);
  MoveTo(2, 480);
  LineTo(2, 0);
  LineTo(0, 10);
  LineTo(4, 10);
  LineTo(2, 0);
  SetColor(LightGray);
  for i := 0 to 6 do Line(i*100+2, 476, i*100+2, 478);
  for i := 0 to 8 do Line(1, i*53+3, 3, i*53+3);
  SetColor(White);                          { (0, 0) equ (2, 477) }
  OutTextXY(9, 425, '100');
  OutTextXY(9, 371, '200');
  OutTextXY(9, 319, '300');
  OutTextXY(9, 264, '400');
  OutTextXY(9, 212, '500');
  OutTextXY(9, 160, '600');
  OutTextXY(9, 105, '700');
  OutTextXY(9,  53, '800');
  OutTextXY(99, 465, '1');
  OutTextXY(199, 465, '2');
  OutTextXY(299, 465, '3');
  OutTextXY(399, 465, '4');
  OutTextXY(499, 465, '5');
  OutTextXY(630, 465, 't');
  OutTextXY(9, 3, 'x');
  OutTextXY(9, 465, '0');
  OutTextXY(599, 465, '6');
end;
{ Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û=Û }
begin
  D:=Detect;
  InitGraph(D,R,'');
  e:=GraphResult;
  if e <> 0 then
    begin
      WriteLn('Îøèáêà ãðàôèêè(', e, '):');
      WriteLn(GraphErrorMsg(e));
      Halt;
    end;
  eps := 0.5E-3 ;
  t := t0-0.5;
  DoScreen;
  C := exp(4.0)*(49766.0/4913.0);
  C1:=56.0/289.0;
  C2:=106.0/289.0;
  C3:=646.0/4913.0;
  C4:=4445.0/4913.0;
  SetColor(Yellow);
  OutTextXY(350, 1, 't      Âû÷. çíà÷åíèå  Ïðèáë. çíà÷åíèå');
  While (t<=b+0.5) do
    begin
      x:=ff(t);
      t := t+0.001;
      PutPixel(Round(2.0+ScaleT*t),Round(477.0-ScaleX*x), Yellow);
    end;
  x := x0;
  t := t0;
  h := h0;
  N := 1;
  While t <= b do
    begin
     Repeat
      tt := t+h/2.0;
      k1 := h * f(t, x)/2.0;
      k2 := h * f(t+h/2.0, x+k1/2.0)/2.0;
      k3 := h * f(t+h/2.0, x+k2/2.0)/2.0;
      k4 := h * f(t+h, x+k3)/2.0;
      S := (k1+2.0*k2+2.0*k3+k4)/6.0;
      x1 := x + S;
      k1 := h * f(tt, x)/2.0;
      k2 := h * f(tt+h/4.0, x+k1/2.0)/2.0;
      k3 := h * f(tt+h/4.0, x+k2/2.0)/2.0;
      k4 := h * f(tt+h/2.0, x+k3)/2.0;
      S := (k1+2.0*k2+2.0*k3+k4)/6.0;
      xk := x1 + S;
      delta := Abs((xk-x)/15.0);
      if delta>eps then
         h := h/2.0;
     Until delta