,,,
-
:
ɠ
.-29 ..
... ..
2001
充..3
1. 4
2. ..6
2.1. 6
2.2 .12
3. 14
4. ..15
5. ...17
5.1. ...17
5.2. .19
20
..21
1 22
2 23
3 24
4 25
, , : , , , , - , .
, : , - , , - , . , , . - . , .
, - .
- .
1.
:
(1.1)
:
= (1.2)
N x N .
- N , ;
N ;
- N .
Ѡ - , . 蠠 , ..
2.
2.1.
, .
:
, (2.1.1)
(2.1.1) y(x) , , :
(2.1.2)
, p(x) ,
頠 f(x,y(x)) .
, , -
.
, Xi
h .
fi = f(xi,yi), ( i=k,k-1,k-2,,k-N) f (x,y(x)) P
(xi,fi) ,
( i =k,k-1,k-2,,k-N) . , P N , P(xi)=fi , ( i = k,k-1,k-2,,k-N) . , , :
(2.1.3)
, N=0 , P , fk , (2.1.3) :
(2.1.4)
N=1 , P ,
(xk-1,fk-1) (xk,fk) , ..
(2.1.5)
Xk Xk+1 , :
(2.1.6)
, xk 蠠 xk-1 . , N=2 , P - , :
(2.1.7)
, (2.1.6) - , (2.1.7) - .
(2.1.7) . . , :
, , . , , .
, , . . .
, - , : [1],[2],[3] , :
:
(2.1.8)
:
(2.1.9)
h - , :
,
- , h=h*N - , h=h/N , N - .
, , , :
(2.1.10)
, , - . : , , - , .
- Xk . , , Xk+1,Xk+2, . Xk+1,Xk,,Xk-N
N+1 , P(Xi)=fi , (I=k+1,k,,k-N) . , - . N=0 , p , (Xk,fk) (Xk+1,f k+1) , :
(2.1.11)
- [2] , (2.1.9) . N=2 , p , :
(2.1.12)
- . , fk+1 , -ࠠ (2.1.11),(2.1.12) . - .
(2.1.7) , (2.1.12) , , - :
(2.1.13)
, 젠 . - , 씠 . 젠 , - . - , - .
:
A =
NxN ; - N , . , A , , , , 2.2 .
, : , , , - (2.1.13) , [2] , [3] .
2.2
, .
: (2.2.1)
1) X1
2) : 2-
1- , 3- 2- , 4- 3- :
(2.2.2)
3) 蠠 , :
(2.2.3)
X1 X2 , - (2.2.1) (2.2.2) .
3.
. , , , , , , - .
. , .
, Yk+1 , , . , - , .
, , .
- 1 .
4.
, - - . VFH , .
PACM , TApplPandC , - Application - ; Done , , .
PACM - . - , , PACMBtn .
Tobject . VFH Tform . TForm - TApplPandC . : MouseHandler : Boolean , FormCreate - . Application - , , .
, PACMMenu , , , PrandCo M Help System . TMenu , THelpForm , VFH .
PACMBtn . - , - MethodAdamsaBashforta ( h,tp,ta : real ; NU : array[1..N] of real ) : h - ; tp , ta - , NU . , . prandcom*.df . , , , - TCartFile , Tform , Tchart .
, ࠠ PrandCo M version 2.41 - Borland Pascal . , . - , .
, 1% .
PrandCo M version 2.41 4 .
5.
:
5.1.
y(0)=1 , 0<=x<=1 , h=0.1 . , :
, .. . 1 . , , 2% . , . , , - . 2 . , , , 1% .
1
2
0.1 | 1.683 % | 0.0250 |
0.01 | 1.163 % | 0.0100 |
0.001 | 0.744 % | 0.0040 |
0.0001 | 0.568 % | 0.0032 |
0.00001 | 0.451 % | 0.0025 |
0.000001 | 0.723 % | 0.0040 |
0.0000001 | 0.578 % | 0.0032 |
0.00000001 | 0.462 % | 0.0026 |
0.000000001 | 0.740 % | 0.0041 |
0.0000000001 | 0.592 % | 0.0033 |
0.00000000001 | 0.473 % | 0.0026 |
2 .
5.2.
.
, - :
:
. h=0.00001 , tp=0.1 - ta=1 .
2 . , .
3 .
- - .
, - .
, .
.
2... 蠠
: .: .. .-
.....1968.-203 .
3. .. .
. .-..1982.-238.
1 :
-
+
|
|
2:
3 :
1- 堠 2
3 堠 4
4 :
{
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| PrandCoM version 2.41 Copiright ( c ) 2001 |
| 젠 |
| ࠠ |
| " " |
| - 29 |
| 젠 |
| ( ) |
| .. |
| NetMail ( FidoNet ) 2:461/212.21 |
| E-Mail : JVUMailbox@rambler.ru |
| |
| VFH version 4.XX |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
}
{$M 10000,0,0}
(****************************************************************************)
(****** : 05.05.2001 **********************)
(****************************************************************************)
Program Prognoz_and_Correction_Modification;
(****************************************************************************)
Uses PACM;
(****************************************************************************)
var
TPC : TApplPandC;
(****************************************************************************)
(******************************) begin (*************************************)
TPC.Application;
TPC.Done;
(*******************************) end. (*************************************)
(****************************************************************************)
{
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| 2.XX |
| |
| " " - 29 |
| - .. |
| NetMail ( FidoNet ) 2:461/212.21 |
| E-Mail : jvumailbox@rambler.ru |
| |
| VFH version 4.XX |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
}
(****************************************************************************)
(**** : 15.04.2001 *****************)
(****************************************************************************)
(****************************************************************************)
(*******************************) Unit PACM; (*******************************)
(****************************************************************************)
(*******************************) INTERFACE (********************************)
(****************************************************************************)
Uses FormObj,MouseObj,PACMEr,PACMMenu,PACMBtn,PACMPnl,PACMPC,PACMCnst;
(****************************************************************************)
type
TApplPandC = object ( TForm )
Function MouseHandler : boolean;Virtual;
Procedure FormCreate;Virtual;
Procedure Application;
end;
(****************************************************************************)
(******************************) IMPLEMENTATION (****************************)
(****************************************************************************)
Procedure TApplPandC.FormCreate;
var
Pnl : TPanel;
Pnl1 : TPanel;
TMenu1 : TCreateMenus;
begin
Pnl.Init(548,35,619,50,1,7,1,1,1,1,false,false);
Pnl.Panel;
Pnl1.Init(470,407,630,460,1,7,1,0,1,4,true,false);
Pnl1.Panel;
TPnl1.ToolBarCreate;
TPnl1.PanelCreate;
TPageControl1.PageControlCreater;
TBitBtns.BitBtnCreaters;
TMenu1.MenusCreate;
end;
(********************************)
Function TApplPandC.MouseHandler;
var
TMouse1 : TMouse;
b,x,y : word;
TMenu1 : TCreateMenus;
TSubMenu1 : TCreateMenus;
ST1 : TSystemTime;
begin
MouseHandler:=false;
TMouse1.GetMouseState(b,x,y);
ST1.Init(549,36,618,49,1,15);
ST1.SystemTime;
TBitBtns.BitBtnHandlers(b,x,y);
MouseHandler:=fExitBtn;
TMenu1.MenusVisible(x,y);
TMenu1.MenusHandlers(b,x,y);
TPageControl1.PageControlHandlers(b,x,y);
end;
Procedure TApplPandC.Application;
var
TIEr : TInitErrors;
begin
TIEr.FatalErrorVFH;
TIEr.LoadFont('km_defj8.fnt');
TIEr.FindImEr1('x.bi');
InitObjGraph;
if InitMouseJVU then
begin
TIEr.LfLoad('Lf.sys');
TIEr.ErrorExec('x.bi');
TIEr.FindFile('f1.dat');
TIEr.FindFile('f2.dat');
TIEr.FindFile('f3.dat');
TIEr.FindFile('f4.dat');
TIEr.FindFile('km_defj8.fnt');
TIEr.FindFile('f_nfrj8.fnt');
TIEr.FindFile('t_nfrj8.fnt');
TIEr.FindFile('asdf.bi');
TIEr.FindFile('pacm_n1.bi');
TIEr.FindFile('pacm_n2.bi');
TIEr.FindFile('pacm_n3.bi');
TIEr.FindFile('pacm_n4.bi');
TIEr.FindFile('PrandCoM.hlp');
TIEr.FindFile('litj.chr');
TIEr.FindFile('scri.chr');
TIEr.FindFile('trip.chr');
TIEr.FindFile('tscr.chr');
TIEr.FindFile('initm.mtr');
TIEr.FindFile('initnu.mtr');
if not fQuickHalt then
begin
TIEr.LoadCFG('PrandCom.cfg');
With HT do
begin
hx1:=575;
hy1:=20;
hx2:=637;
hy2:=34;
hc:=true;
hs:='';
end;
Init(1,1,639,479,7,1,'Prognoz & Corrections Modifications');
Form;
end;
end
else
begin
TIEr.ErrorVFH;
end;
end;
(****************************************************************************)
(***********************************) END. (*********************************)
(****************************************************************************)
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