: ? . , , . MathCAD . , , , . . , , MathCAD. 5.1 1- -.
5.1 -
-
rkfixed
MathCad rkfixed.
MathCad:
, :
y = f (x, y) (5.1)
n , :
(5.2)
;
, .
:
rkfixed (y, x1, xk, k, D),
y - n, n - . y0 ( y');
x1, xk - , . , y, - x1;
k - ( ), . (k + 1) , rkfixed;
D (x, y) - -, n , ( (5.2) (5.1)).
rkfixed - . , n +1 :
, ( x);
y1(x), - y2(x) ..
5.2 , 5.3 - .
5.2 -
5.3 -
, (5.2). ,
|
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y(n)= f(x,y(n-1),y(n-2),,y)
(5.2):
5.4 , 5.5 - , (5.2), .
1. [ 0, 2 ]:
.
1. : y → y0, y' → y1, y'' → y2, y''' → y3
2. , :
5.4 -
2. [ 0, 0.4 ]:
u(x), v(x).
1. : u → y0, u' → y1, v → y2, v' → y3
2. , :
5.5 -
odesolve
MathCad 2000 , , Given :
odesolve(x,b,[step])
:
x ;
b ;
step - , .
: Given, . odesolve, , . , MathCad- , , , , , . 5.6 .
5.6 -
odesolve
d/dx, d2/dx2 y¢(x), Ctrl/F7.
, , y(a)=b y¢(a)=b, y¢(a)+y(a)=b.
odesolve , , , .
5.7 3- odesolve.
5.7 -
odesolve
Bulstoer, Rkadapt
, ,
Bulstoer (y, x1, xk, k, D),
-, -, rkfixed. .
, , , - .
Rkadapt (y, x1, xk, k, D).
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rkfixed, , Rkadapt , , , , . , , - , . , .
, , Rkadapt , .
, , rkfixed.
bulstoer, rkadapt
, , y(x) [x1, xk]. , , . , , y (xk), , y(x). y (xk), , . , .
:
bulstoer (y, x1, xk, e, D, kmax, save)
rkadapt (y, x1, xk, e, D, kmax, save),
y - ;
x1, xk - , ;
D - -, ;
e - , . e , . e, 10 -3 - 10 -5 ;
kmax - , . kmax , ;
save - , . , .
5.8 .
5.8 - rkadapt