                               2

       祭  ᯮ ,  뢠  "
騪",    ⥬  ன  室  室,   ,  
ந室  - ⭮.    ந室 
室  ᨣ   ᨬ  室   ࠧ묨,  
⮬ ᫥     ७樠 .  ⠥ ஡-
 襭 ⥬ ७樠 ࠢ,    ᨬ
 ᢮    襭 ࠧ묨 ⮤. 筮 -
   祭   㤠,  ⮬  ᬮਬ ᫥
⮤ 襭 ⠪ ⥬.    ।⠢  㯯  ⮤:
  .  襭 ⥬  묨 ⮤ ਤ -
 ⥬  ࠢ,  ⮬ ਤ   ᬮ-
७  㯯  ⮤ 襭 ⥬  ࠢ,   
᢮ ।  ।⠢  ⮤.  ᫥ ⥮-
᪨ ᯥ ᠭ ⮤,   ⥬  ।⠢ ᠭ
ணࠬ.  ணࠬ,  ⠪  䨪 ਢ  ਫ.
      ⮨ ⬥,   ਭ樯  ᫥ ⮤ ⠪ 
 ᢮  筮 ,    ᪨    祭
     ᫠   訥 ࠧ  ⮬
䥪⨢ ࠡ  묨 栬.    孮, -
 ࠧ    ஡  -  孮  ࠧ० .
 裡  ⨬,  ᬮਬ  孮  樨 㬭 
࠭ᯮ஢  ⠪ 栬.
      ࠧ  ᬮਬ  ᯥ  ࠡ.  -
ᠭ   ணࠬ ਢ ᫥ ⥮᪮ .   ⥪
ணࠬ  ᯥ⪨ 䨪 ਢ  ਫ.

                         2 

              1.     
                             

                       

         ⮣ ⮤ । 㫮:
                    x5m+10 = x5m0 + h4m0*F(x5m0, t4m0)4,0                    (1)
   砥  பᨬ樨 鸞   童 ࢮ-
   浪 ந x'(t4m0),.. 冷 筮 ࠢ 1 (s=1).
         ᪮ ᫥ ᢮ ⮤  -
   室 ⥬   x' = F(x, t)   窥 (x5m0,t4m0):
                         x' = A*x,                               (2)
       窨 ਧ樨 (x5m0,t4m0).
        室 ᨣ  ਧ樨  ⭮  㭪樥
  ६     䨪஢ t4m0  蠣 h4m0   ⠭-
  ⮩.  ⮣ ,   ⥬ ᢮⢮ ⮩稢  -
     ,  室 ᨣ  ⥬ (2)  . -
        窨 ਧ樨,..  -
   m.

        ࠪ⨪ ⮤:
        1. _᫥ ⮩稢..
        ਢ    쭮 ଥ :  = *7l0*5-10  ३
    ६   y = P5-10*x , ⥬ (2) ਬ  :
                            y' = 7l0*y                               (3)
         ⮤   ࠢ (3) 㤥   :
                         y5m+10 = y5m0 + h*7l0 * y5m0,                     (4)
   稭 h*7l0   蠣  蠣.
         ⮬ 砥 ࠪ᪮ ࠢ  ⭮ -
  ⥬ (4) 㤥   :
                        1 + h*7l0 - r = 0.
   ७ ࠪ᪮ ࠢ ࠢ:
                        r = 1+ h*7l0,
   7l0 =7 a0 _+.7 b0 .
        _砩 1.. 室 ⥬ (3)  ᨬ᪨ ⮩-
  稢 , .. 㫥 ﭨ ࠢ ⥬ ᨬ᪨ -
  ⮩稢  7 a0 < 0.
         ᮫⭮ ⮩稢 ⮤ ⥣஢ ⥬
  (4) 㤥  ࠤᮬ ,  ࠢ 1 ,    業஬  窥 (0,  -1).
   ࠧ , 蠣 h    ࢠ ⥣஢ -
   ⠪ ࠧ,  ⮡  ⮬      .  
   ⠪ 砥  믮 ॡ :
                            h < 2*7t0,                               (5)
   7t0=1/72a20  - ﭭ ६ ⥬ (3) .   । ᪮-
   堭 室 ᮢ  .  ६ 室 -
   T40 = 3*7t0 ,  7t0 = 72a25-10.
        ᫨  ,  ⥬ (3) n- 浪, 
                         T40 > 3*7t4max0,
   7t4max0 = 72a4min725-17 0; 7a4min 0= min 7a4i0 .   7a4i0 (i=[1;n]) 롨ࠥ-
   ᨬ쭮 祭 : max72a4i720=7a4max0   ⮣  ᫨ :
                        7t4min 0= 1/7a4max0,
   蠣  롨 ᫥騬 ࠧ :
                   h < 2/7a4max0     h < 2*7t4min0.
        _砩 2..  㫥 ﭨ ࠢ ⥬ (2) ⮩-
  , .. 7a0 > 0 . .. ⥬ ⮦ ⮩稢 , .. 720r720>1. ⮬
   ⭮⥫쭮  ⮩稢    ⮤  
   ࠢ 㯫᪮ . 믮 ॡ :
                    720 1+h*7l0 72 0<7 2 0e5hl7 20                            (6)

        2. _筮 ⮤..
           㫠 ⥣஢ (1) பᨬ  
   㭪樨 x(t4m0+1)    h 童 ⥫쭮. 
  ⠪ 祭 t  ࢠ [t4m0 , t4m+10],  ஬
                      4i5am0 =1/2! * h4m520*x4i0''(t),
   i=[1;n].

        3. _롮 蠣 ⥣஢..
         ᮡ ᫮ ᮫⭮  (5)    ⭮⥫쭮
  (6) ⮩稢  ᨬ  ࠪ ⥣㥬 ⥬.
         ࠢ ࢮ 浪 蠣   :
                              h < 2*7t0 .
         ࠢ n- 浪 :
                             h4i0 <= 2*7t4i 0.
   ⥫쭮 蠣 롨  ᫮ ⮩稢 :
                    h < 2*7t4min0 ,  7t4min0 = min 7t4i
  砫  ⨬ 訡 பᨬ樨 ,     -
  ⥣஢ 蠣 ࠥ ᫥騬 ࠧ :
        1)  㫥 (1) । । 祭 x5m+10;
        2) । dx4i5m0 = x4i5m+10 - x4i5m0 ;
        3) ᫮ ᮡ 筮   :
                h4i5m0 <= E4i5a7/0[720f4i0(x5m0,t4m0)720 + E4i5a7/0h4max0]           (7)
        4) ⥫쭮  m- ࢠ ६ 롨ࠥ  :
                              h4m0 = min h4i5m0.


                         -

        ⮤     ⮤  㭣-  1-  浪  .
  ⮤ 㭣-  2-    4-  浪    蠣묨 ,
  ᮣ  冷   浪 筮 s  ,    ࠢ
  浪 ⮤  .    ⮤    ॡ  ᫥  ந
  㭪権 ,  ⮫쪮 ᠬ 㭪樨  ᪮쪨 窠  蠣 h4m0.
         ⮤ 㭣- 2- 浪 ⮨  ᫥饬 :
                x5m+10 = x5m0 + h4m0/2 (k410+k420),
   k410=f(x5m0,t4m0) ; k420=f(x5m0+h4m0*k410,t4m0+h4m0).
        訡 பᨬ樨 5a0 = k*h4m530 .
         ⮤ 㭣- 4- 浪
                x5m+10=x5m0+h4m0/6(k410+2k420+2k430+k440),
   k410=f(x5m0,t4m0); k420=f(x5m0+h4m0/2*k410,t4m0+h4m0/2); k430=f(x5m0+h4m0/2*k420,t4m0+h4m0/2);
                       k440=f(x5m0+h4m0*k430,t4m0+h4m0).
        訡 பᨬ樨 5a0 = k*h4m550.

                   

          ⮤  ᯮ  ⥣஢  " -
   " ⥬. "⪨" ⥬  ⠪ ⥬,  7 0 (7l4max0)
   (7l4min0) ᨫ쭮 ⪫   㣠 ,   襭 ⥬
                           x' = A*x                              (1)
   ⢮ ᯮ,  ᨫ쭮 ⫨   㣠 
  ᪮ 堭 .   ⥣஢  ⠪ ⥬  -
    ᫮ ⮩稢  ࠢ⢠
                          h <= 2*7t4min ,0                          (2)
   7t0=1/72a20  - ﭭ ६ ⥬  y' = 7l0*y .  ।
  ᪮ 堭  室  ᮢ     .  ࠢ⢮ (2)
   믮  ᥬ ⪥ 襭 ,  ᮮ⢥⢥ -
   ⥫  設 ६.
          ⮣ ⮤ । 㫮:
                    x5m+10 = x5m0 + h4m0*F(x5m+10, t4m+10) 4                0(3)
         ᫨ h4m0 ,  x5m0  5m+10    .  ⢥ -
  砫쭮 ਡ  窠 x5m0 ,  ᫥⥫쭮 ,  x5m0 
  x5m+10 㤥 ⢮ 樮 .

         ᪮  ᫥ ᢮  ⮤  -
  ਧ 室 ⥬   x' = F(x, t)   窥 (x5m0,t4m0):
                         x' = A*x,
       窨 ਧ樨 (x5m0,t4m0).
        室 ᨣ  ਧ樨  ⭮  㭪樥
  ६     䨪஢ t4m0  蠣 h4m0   ⠭-
  ⮩.  ⮣ ,   ⥬ ᢮⢮ ⮩稢  -
     ,  室 ᨣ  ⥬ (1)  . -
        窨 ਧ樨,..  -
   m.

        ࠪ⨪ ⮤:
        1. _᫥ ⮩稢..
        ਢ    쭮 ଥ :  = *7l0*5-10  ३
    ६   y = P5-10*x , ⥬ (3) ਬ  :
                            y' = 7l0*y                             (4)
         ⮤   ࠢ (4) 㤥   :
                         y5m+10 = y5m0 + h*7l0 * y5m+10,                 (5)
   稭 h*7l0   蠣  蠣.
         ⮬ 砥 ࠪ᪮ ࠢ  ⭮ -
  ⥬ (5) 㤥   :
                        1 - h*7l0*r - 1 = 0.
   ७ ࠪ᪮ ࠢ ࠢ:
                         r = 1/(1-h*7l0) ,
   7l0 =7 a0 _+.7 b0 .
        _砩 1.. 室 ⥬ (4)  ᨬ᪨ ⮩-
  稢 , .. 㫥 ﭨ ࠢ ⥬ ᨬ᪨ -
  ⮩稢  7 a0 < 0.
         ᮫⭮ ⮩稢 ⮤ ⥣஢ ⥬
  (5) 㤥   㯫᪮.  ࠧ , 蠣  h   
   ࢠ ⥣஢  ⠪ ࠧ, ⮡ 
  ⮬    .    ⠪ 砥   믮
  ॡ :
                            h < 2*7t0,                             (6)
   7t0=1/72a20  - ﭭ ६ ⥬ (4) .   । ᪮-
   堭 室 ᮢ  .  ६ 室 -
   T40 = 3*7t0 ,  7t0 = 72a25-10.
        ᫨  ,  ⥬ (4) n- 浪, 
                         T40 > 3*7t4max0,
   7t4max0 = 72a4min725-17 0; 7a4min 0= min 7a4i0 .   7a4i0 (i=[1;n]) 롨ࠥ-
   ᨬ쭮 祭 : max72a4i720=7a4max0   ⮣  ᫨ :
                        7t4min 0= 1/7a4max0,
   蠣  롨 ᫥騬 ࠧ :
                   h < 2/7a4max0     h < 2*7t4min0.
        _砩 2..  㫥 ﭨ ࠢ ⥬ (4) ⮩-
  , ..  7a0  >  0  .  ..  ⥬ ⮦ ⮩稢 ,  ..  720r720>1,
   ᫥⥫쭮 :
                         720 1/(1-h*7l0) 720 > 1.
          ⮬ ࠭祭  ᪮  ਡ  -
  襭 ⭮⥫쭮 筮 :
                     720 1/(1-h*7l0) 720 >7 2 0e5hl7 20.                    (7)
          ⮣ ᮮ⭮襭 ᫥ ,   720h*7l20 -> 1  
  ६  ᪮筮 .  砥 ,   ࠢ 㯫᪮-
      ࠤᮬ , ࠢ 1 ,     業஬    窥
  (0, 1),  ࠢ⢮ (7)  믮.

         2. _筮 ⮤..
         訡 பᨬ樨    稭 ࠢ 訡 பᨬ樨
   ⮤  ,   ⨢   :
                      4i5am0 =-1/2! * h4m520*x4i0''(t),
   t4m0 <= t <= t4m+10,
      i=[1;n].

         3. _롮 蠣 ⥣஢..
          ᮡ ᫮ ᮫⭮ (6)    ⭮⥫쭮
  (7) ⮩稢  ᨬ  ࠪ ⥣㥬 ⥬.
          ࠢ ࢮ 浪 蠣   :
                              h < 2*7t0 .
          ࠢ n- 浪 :
                             h4i0 <= 2*7t4i 0.
           ᮫⭮ ⮩稢 -    㯫-
   . ⮬ 蠣  ⮩ 窨 ७   .
         ᫮ ⭮⥫쭮 ⮩稢 ,  ⠪    -
   ,     襭.  ᫮  믮 ,
  ᫨   襭  ஫஢ 訡 பᨬ樨 ,
   蠣 ४஢ .   ࠧ, 蠣  롨  ᫮
  筮,  ⮬ ᫮ ⮩稢  ᮡ ⮬-
  . 砫  ⨬ 譮 பᨬ樨 :
                    E4i5a0 <= 0,001 720x4i724max0,
   i=[1;n].

          롨ࠥ   ⥣஢ ᫥騬 ࠧ:
         1.  ⥬ (3) ⭮⥫쭮 x5m+10  蠣  h4m0,  砥
  ।  襭 ⥬ x = F(x,t) ;
         2. 業 稭 訡 பᨬ樨  㫥:
      4i5am0 =  720h4m7/0(h4m0+h4m-10)*[(x4i5m+10  - x4i5m0) - h4m7/0h4m-10*(x4i5m0 -x4i5m-10)]72
         3. ⢨⥫쭮 祭 பᨬ樨 ࠢ    -
  ⨬. ᫨ 4i5am0 < E4i5a0,  믮 ᫥騩 㭪,  -
  ⨢ 砥 蠣 㬥蠥   ࠧ ,   ᫥ 
   .1.
         4. 뢠 ᫥騩 蠣:
                h4i5m+10 = SQR(E4i5a7/204i5am720) * h4m0.
         5.  롨ࠥ    ⮢  X :
                              h4m+10 = min h4i5m+10.
         6.    ६    .



                         -

         ⮤     ⮤  㭣-  1-  浪 .
  ⮤ 㭣-  2-    4-  浪    蠣묨 ,
  ᮣ  冷   浪 筮 s  ,    ࠢ
  浪 ⮤  .    ⮤    ॡ  ᫥  ந
  㭪権 ,  ⮫쪮 ᠬ 㭪樨  ᪮쪨 窠  蠣 h4m0.
          ⮤ 㭣- 2- 浪 ⮨  ᫥饬:

                x5m+10 = x5m0 + h4m0/2 (k415m+10+k425m+10),
      k415m+10=f(x5m+10,t4m+10);  k425m+10=f(x5m+10-h4m0*k415m+10,t4m+10).
         訡 பᨬ樨 4m5a0 = k*h4m530 .
          ⮤ 㭣- 4- 浪

                x5m+10 = x5m0 + h4m0/6 (k415m+10+2k425m+10+2k435m+10+k445m+10),
      k410=f(x5m+10,t4m+10);     k420=f(x5m+10-h4m0/2*k415m+10,t4m+10-h4m0/2);
         k430=f(x5m+10-h4m0/2*k425m+10,t4m+10-h4m0/2);     k440=f(x5m+10-h4m0*k435m+10,t4m0).
         訡 பᨬ樨 5a0 = k*h4m550.


                   2.    

                             

     樮 㫠 ⮤ ⮭  
                     X5m+10=X5m 0-5 0J5-1 0*5 0(X5m0)5 0*5 0F(X5m0),
      J(X)=F4x5|0/4x=xm
     ࠪ⨪ ⮤:
     1. 室. ,   窥 P(G4x5|0(X5*0))=0
      G(x)=X  - J5-10(x) * F(x) - ࠦ 樮 -
. ᫮ 室 ⮤:  P(G4x5|0(X)) < 1   믮  
 祭  X5m0.    ᫮ ⢫  筮 ⪨
ॡ  F(x):  㭪   뢭   ७㥬
 X,  ⠪ 㪫    X5*0.  ⮬ 믮 
᫮ 쭮 室.  祬  ,   祬  
X5*0, ⥬ ॥ 室 ⮤.
     2. 롮 砫쭮 ਡ X500 - 롨ࠥ 筮 
 筮  襭.     -   ᪮ 
㭪樨 F(x)  X5*0:  祬  ᪮,  ⥬   ,  
ᮡ ᫮  室  ᫥⥫쭮 室  롨-
 X500  X5*0.
     3.  室 । ᮮ⭮襭
                  E5m+10 = C4m0 * E5m051+p0,  0 < P < 1.
      X -> X5*0 稭 P -> 1.  ,   筮 -
 ᪮ 室   筮.  ⭮,    ⮤
⮭ 室  6-7 樨.
     4. ਩ 砭 権 -   ᯮ짮  -
ਨ 筮,   ᨬ쭠    X  F(x).

                         

     㤭 ᯮ짮 ⮤ ⮭ ⮨ 
     1. 室 ᫥   ⠯ J=F4x5|0.
      ᪮쪮 ⥩ 襭:
     - ᪨ ᯮᮡ.  䥪⨢,   -
   ᫨誮 訬,  ⠪ 㭪樨    ⠡-
筮.
     - 筮-ࠧ⭠ பᨬ:

       dF4i0   F4i0(x410,...,x4j0+dx4j0,...,x4n0) - F4i0(x410,...,x4j0-dx4j0,...x4n0)
        = 
       dX4j0                           2*dX4j

      ⮬ 砥   㦥  ⮤ ⮭,   㦥
  筮 室.  室  㢥-
, 㬥 dX4j0   ਡ  X5*0.
     2. ᫥  J5-10   蠣 ॡ ⥫ -
᫨⥫ , ⮬   ⠪ ⥬:
                         dX5 0=5 0J5-10(X5m0)5 0*5 0F(X5m0)
      㬭 ࠢ     J, 稬:
                         J(X5m0)5 0*5 0dX5m 0=5 0F(X5m0)
       M- 蠣  J  F . 室  dX5m0,
 襭 襯ਢ ⥬  , ⮣
                             X5m+10=X5m0+dX5m
     ᭮ ⮪  ⮤  ⮭  -  쭠 室,
⮬ ᬮਬ   ⮤.

                    

      t - ࠬ,  騩  0  1.    ᬮ७
 ⥬
                              H(X,t)=0,
     ⠪, :
     1.  t=0 ⥬  襭 X50
     2.  t=1 ⥬  襭 X5*
     3. -㭪 H(X,t) 뢭  t.
      㭪   ࠭ ᪮쪨 ᯮᮡ, ਬ
                        H(X,t) = F(X) + (t-1)
                                 
                          H(X,t) = t * F(X)
     㤭 ஢,    -㭪権 믮 ᫮-
 1-3.
      ⮤ ⮨  ᫥饬:
      t410=7D0t  蠥 ⥬ H(X,t410)=0  ࠭ X500. -
砥   X5t10.   ६   ⢥ 砫쭮 ਡ 
蠥   t420=t410+7D0t ⥬ H(X,t420)=0,  砥 X5t20  ⠪ 
  ,   㤥 ⨣  筮.

                   3.   

                          .

     ᭮ ॡ  ⨬ ⮤  ᢥ  3 ⢥ত:
     1. ࠭   ⮫쪮 㫥 .
     2.   襭 ਭ , 㬥騥  -
  㫥 ⮢.
     3. ᫥ ந ⮫쪮  㫥묨 ⠬.

                     ०  ଠ

          ப  ᯮ㥬  奬  ࠭ ࠧ०
,  ।  ॡ       祭
㤮  믮 ᭮ 権  栬.
     祭 㫥 ⮢  ᮮ⢥騥 ⮫殢 
࠭   ப    ᨢ:  NA  JA.   ࠧ⪨ ப 
 ᨢ ᯮ ᨢ 㪠⥫  IA,  ⬥  樨
ᨢ AN  JA,   稭 ᠭ । ப. -
   ᨢ IA ᮤন 㪠⥫ ࢮ ᢮  樨
 JA  AN.  ᬮਬ  ਬ,   㤥 ⠪  
ਬ  樨 㣨 権     ᯮ짮
 ⢥  ஫쭮  ਬ  ணࠬ,  믮饩 ᭮
樨  ࠧ०묨 栬.
                     
           3 0 0 5 0       :  1 2  3 4  5 6  7 8  9 10
           0 4 0 0 1            IA:  1    3    5    7    9    11
      A =  0 0 8 2 0            JA:  1 4  2 5  3 4  1 4  2 5
           5 0 0 6 0            AN:  3 5  4 1  8 2  5 6  7 9
           0 7 0 0 9 
                     
      ᯮᮡ ।⠢ 뢠  (⠪   ।⠢-
     )   㯮冷祭 (⠪    ப
࠭  ᮮ⢥⢨  ⠭ ⮫殢 ᮢ). -
 RR(c)O - Row-wise representation Complete and Ordered (.).
     ᨢ IA  JA ।⠢   .  ᫨  ⬥
ࠧ࠭祭 ⠯ ᨬ᪮  ᫥ ࠡ⪨,   ᨢ IA
 JA   ࢮ ⠯,  ᨢ AN -  ஬.

                 ࠭ᯮ஢ ࠧ० 

      IA,  JA,  AN - ஥ ।⠢ ࠧ० .
㦭  IAT,  JAT, ANT - ࠧ० ।⠢ ࠭ᯮ-
 .  ᬮਬ  襬 ਬ:

     IA = 1 3 5 7 9 11
     JA = 1 4 2 5 3 4 1 4 2 5
     AN = 3 5 4 1 8 2 5 6 7 9

     ᪨ ⠯.
     1.  5 楫 ᯨ᪮   ⮫殢  .  ஭㬥-
㥬   1  6.
     2. 室 1 ப  ᨬ 1   ᯨ᪨,    㪠-
  JA:
                        1: 1
                        2:
                        3:
                        4: 1
                        5:
     3. 室  ப, ⠢  ࠧ 2:
                        1: 1
                        2: 2
                        3:
                        4: 1
                        5: 2
      ⮣ 稬:
                        1: 1 4
                        2: 2 5
                        3: 3
                        4: 1 3 4
                        5: 2 5
     ᨢ ANT  ,  ⠢ ᫥  祭  
, ࠭  AN,   ⢥ ᯨ᮪ ࠧ ᫥ ⮣,  ᮮ-
饥 楫 ᥭ  楫 ᯨ᮪.  ⮣ 稬:
     IAT = 1 3 5 6 9 11
     JAT = 1 4 2 5 3 1 3 4 2 5
     ANT = 3 5 4 7 8 5 2 6 1 9

                  ந ࠧ०  
                      -⮫

      ᬮਬ  襬 ⭮ ਬ:
     IAT = 1 3 5 7 9 11
     JAT = 1 4 2 5 3 1 3 4 2 5
     ANT = 3 5 4 7 8 5 2 6 1 9
     B = ( -5 4 7 2 6 )
     ࠡ⪠ 1 ப:
     ᬠਢ ᨢ IA  㦨,  ࢠ ப 
 ᮮ⢥  ࢮ    ஬    ᨢ  JA:  JA(1)=3,
JA(2)=4,     a4110  a4140.
     ᬠਢ ᨢ AN  ⠭,  a4110=3  a4140=5.
     頥   B,  롨   ᮮ⢥⢥  b410=-5  
b440=2.
     塞 C410= 3 * (-5) + 5 * 2 = -5.
     ᮫⭮ 筮,  ⠫ ப, 稬:
                         C = (-5 58 56 1 58).

                 ந  ࠧ० 

     ᬮਬ ⮤  ⭮ ਬ.  ।,   -
室 ६  :

     IA = 1 3 5 7 9 11
     JA = 1 4 2 5 3 4 1 4 2 5
     AN = 3 5 4 1 8 2 5 6 7 9

     IAT = 1 3 5 7 9 11
     JAT = 1 4 2 5 3 1 3 4 2 5
     ANT = 3 5 4 7 8 5 2 6 1 9

      ⮤ ⮨  ⮬,  ᯮ ⮤ ६ ४-
⥫  ७ ⢥ ⥫,  冷 -
 㬬  ନ஢ ⮢  .   㤥 ନ-
  C4ij0  ࠧ,   ⥯ ,  ⮫쪮
 ப  B.

     ᪨ ⠯.

     ।塞 ୮ IX = 5
     IX = 0 0 0 0 0

     1- ப  JAT: 1 4
       JA(1) = 1 4      JC(1) = 1 4
       IX = 1 0 0 1 0
       JA(4) = 1 4
       IX(1) = 1 ?  . JC(1) -  
       IX(4) = 1 ?  . JC(1) -  
     2- ப  JAT: 2 5
       JA(2) = 2 5      JC(2) = 2 5
       IX = 1 2 0 1 2
       JA(5) = 2 5   -> JC(2) -  
     ....
     4- ப  JAT: 1 3 4
       JA(1) = 1 4      JC(4) = 1 4
       IX = 4 2 2 4 2
       JA(3) = 3 4
       IX(3) = 4 ? . JC(4) = 1 4 3
       IX(4) = 4 ? .  JC(4) -  
     ....
      ⮣ 稬:
     IC = 1 3 5 7 10 12
     JC = 1 4 2 5 3 4 1 4 3 2 5

     ᫥ ⠯.

     X = 0 0 0 0 0

     1- ப: JC(1) = 1 4
     AN(1) = 3 5,
        AA = 3
           ANT(1) = 3 5
           AA * ANT = 9 15
           X = 9 0 0 15 0
        AA = 5
           ANT(1) = 3 5
           AA * ANT = 15 25
           X = 24 0 0 40 0
     CN(1) = 24 40
     ....
     筮 த뢠 ⢨  㣨 ப 稬:

     IC: 1       3       5      7          10     12
     JC: 1  4    2  5    3  4   1  4  3    2  5
     CN: 24 40   20 35   80 0   55 22 66   16 144

      襯ਢ 樨 뫨 祭       -
 ᮢ   襣 ஫쭮 ਬ.  ᠭ ணࠬ
 몥2 C0,  饩 ⨬ ﬨ  ਢ, ⠪  -
 ணࠬ   ࠧࠡ뢠,   ਫ -
 ᯥ⪠ ⮩ ணࠬ.

                2 .  .

     1.  .
      㯯 ।⠢ 3 ணࠬ, ॠ騬 ⮤ -
,㭣- 2-  4- 浪.    㯯   ணࠬ
, ⮬  ᫥ ᠭ ணࠬ,  ॠ饬 -
⮤ ,   㪠 ࠧ稩  ⮤ 㭣- 2-   4-
浪.
     1EILER.M
      .
     室  室 : .
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     ⠭  .  ந室 ⪠ ࠭,  
砫 祭  ६   Y.  ⥬ ந室 맮 ண-
ࠬ EIL.M (RG2.M  RG4.M  ⮤ 㭣- 2  4 浪) 
᫥ 祭 १⮢  䨪.
     1EIL.M
     ᫨⥫ .
     室 :
     FunFcn -    ணࠬ,  ᠭ  짮⥫,  
頥   ࠢ  ।  ६.
     T0, Tfinal - 砫    ६.
     Y0 - 砫 祭.
     室 :
     Tout - ⮫ ६
     Yout - ⮫ 襭   न
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
         ॠ ᮡ⢥ ⮤  (㭣- 2
 4- 浪).  砫 ந室 樠 ७ -
,  ⠪ ᫥ ᨬ쭮 蠣,  ⥬ ᯮ-
  । 筮.   ᫥ 横 While...End  
ண  믮  室 ⢨:   㫥 ( -
 ⮤ ᢮!)  祭 Y   蠣 (  -
 뢠  㭪  FunFcn)    ⠪ ନ 室
祭 Tout  Yout.  ⮤ ᠬ ४ ᢮ 蠣,  -
 ᠭ  ( ⥮᪮ ࠧ).   横 믮 
 ,  祭 Tfinal  㤥 ⨣.  室 -
 ନ    横  ⮬  ⥫
⢨  ॡ.  裡  ⨬  砭 横 稢
 ணࠬ  EIL.M.  ⮤  㭣- ॠ 筮,  
⮬ ⫨稩  㫠 ᫥ ( ᫮  ࠢ  -
⮤ ).

     2.  .
     ।⠢ 㯯   宦  ᮡ ணࠬ, ॠ-
 ᮮ⢥⢥  ⮤   㭣-  2  浪.
    襯ਢ 砥, 㤥 ᠭ ⮤ ,  -
 ⮤ 㭣-  ⬥祭  ᪮.
     1NME.M
      .
     室  室  .
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     믮 ⠭ ⢨:  ⪠ ࠭,  樠 
 砫 祭,  맮 ணࠬ ࠡ⪨  ᫥,  
⠪ ஥ 䨪.
     1NMEF.M, NRG2.M
     ᫨⥫ 㫨.
     室 :
     T0, Tfinal - 砫    ६
     X0 - -⮫ 砫 祭.
     H - 砫 蠣
     A - ,    ன  ᮡ⢥ ᫠ -
ਧ ⥬ .
     室 :
     T - ⮫ ६
     X - ⮫ 襭
     7D0X - ⮫ 訡
     ᭥  ⥪ :
     ⠭ ⢨:  樠  砫  祭 ,  横
While T < Tfinal,  ᫥  㫠, 뢮 ஬ १-
⮢, ନ஢ 室 祭 ᨢ.

     3.    
     ।⠢ 㯯  4- ⮤: ⮤ ᫥⥫ ਡ-
, ⮤ ⮭,  ⮤ ⮭ ,  ⮤  த
襭  ࠬ.

                 ⮤ ᫥⥫ ਡ.
     1MMPP.M
      .
     室  室  .
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     ⪠ ࠭,  樠 砫 祭, 맮 ᫨-
⥫쭮  MPP.M, 뢮 १⮢   䨪.
     1MPP.M
     ᫨⥫ .
     室 :
     X0 - 砫쭮 ਡ   -ப
     Fun1 - 㭪,  ᫥  
     Fun2 - 㭪,     । 窥.
     E - ⨬ 訡.
     室 :
     Mout -  権
     Xout - ਡ   樨
     DXout - 訡   樨
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     祭 襯ਢ ᫨⥫  - 樠
砫 祭,  ᫥   㫠,  뢮 ஬ -
⮢, ନ஢ 室 祭.   室 -
 ணࠬ Fun1  Fun2.

                 ⮤ ⮭  ⮭ 
     1MNEWT.M
      .
     室  室  .
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     ⠭    -  믮  ⢨,  
।騬  . 뢠  ᥡ NEWT.M  NEWTD.M - -
 ॠ騥 ⮤ ⮭  ⮭ ,   ⠪ ந 
䨪   न⭮ ⪥.

     1NEWT.M, NEWTD.M
     ᫨⥫ 㫨.
     室 :
     X0 - 砫쭮 ਡ   -ப
     Fun1 - 㭪,   
     Fun2 - 㭪,     (⮫쪮  ⮤
                                                             ⮭!)
     E - ⨬ 訡
     室 :
     Mout -  権
     Xout - ਡ   樨
     DXout - 訡   樨
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ 㫥:
     ⠭ ᫨⥫ 㫨,  ந騥  ᮮ⢥騥
 ⢨. ⫨稥   ⮬,   ࢮ 砥  ᫥ -
  뢠 ணࠬ,    ஬ 砥   
  .

                ⮤ த 襭  ࠬ
     1MMPRPP.M
      .
     室  室  .
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     ⠭    ᥬ ⥪騬   ᫥-
⢨ﬨ.
     1MPRPP.M
     ᫨⥫ .
     室 :
     Fun1 -  ணࠬ, 饩 ࠢ 
     Fun2 -  ணࠬ, 饬  
     X0 - 砫쭮 ਡ
     dT - 砫 蠣
     Edop - ⨬ 訡
     Trace - 뢮  ࠭
      ॠ樨: PC MathLab
     樮 ⥬: MS-DOS 3.30 or higher
     ᭥  ⥪ :
     ⠭ ᫨⥫   -  樠,  ᫥,
뢮, ନ஢  १.  ⮨ ⬥,   ᪮ ⮤
  室,   ꥬ ᫥  ⥫,  
 ,   믮 ᫥ ॡ ⥫쭮 -
⢮ ᢮ ⨢ .

                                2

      믮   ࠡ  뫨  祭  ᭮
᫥ ⮤  襭 ,  ,  ⠪ 孮 ࠧ०
.  뫨 祭 ᭮ 모  ணࠬ஢  -
᪮ ⥬  PC  MathLab.     ।⠢ ⮤ 
᢮   ਬ  ⥬ । .
