. : - - .
:
h :
xi = x0 + ih yi = y(xi), i = 0, 1, 2,...,
xi - ,
yi - .
h .
4.
4. .
:
1. : (i, yi,), C(xi + h/2, yi + h/2 ∙ f(xi, yi)) B(xi+1, yi+1);
2. α, tg α = f(xi, yi);
3. (i + h/2, yi + h/2 ∙ f(xi, yi));
4. α1, tg α1 = f(xi + h/2,yi + h/2 ∙ f(xi, yi));
5. , ;
6. B(xi+1, yi+1). B(xi+1, yi+1) = xi+1;
7. , , , i+1:
yi+1 = yi + h ∙ f(xi + h/2, yi + h/2 ∙ f(xi, yi)).
. 4 . εl , ε - .
- 5.
|
.
|
0, X -
|
;
|
y(x0)=y0;
|
:
Y -
|
5. - .
.
.
1. ;
2. A(0; -1.8) ;
3. A:
4. l0 α0;
5. 1 : xi = 0 + ih, h
x1 = 0 + 1 0,2 = 1,2;
6. x = x1 = 1,2 l0, B(x1; y1);
7. y B:
ABC ,
|
|
Δy = y1 y0,
Δx = x1 x0 = h,
f(x0; y0) = (y1 y0)/h =>
y1 = y0 + h (f(x0; y0)) = -1.8 + 0,2 f(0;-1.8) = -1.8 + 0,2 0 = -1.8
, B (1.2; -1.8).