1.
: .
: , , , .
1. , - .
( -) f(x) = 0 xn.
f(x) = f(xn) + (x-xn)∙f(xn) + O(f "(xn)).
O ( order) , .
f(x) ≈ f(xn) + (x-xn)∙f(xn) ≈ 0
, - xn, n - (n ≥ 0), xn+1. (xn) (xn+1) ε, ..
|xn+1 xn| ≤ ε
xn+1 f(x) = 0
, f(x) , . . |f (xn) | ≤εf |f (xn+1) | ≤εf, εf - .
(. 2), .
. 3. .
xn, f (xn) ( ), f (x) . xn+1, . . xn, f (xn) f' (xn) .
(xn - xn+1) ε, . xn+1 , xn+2
|xn+2 xn+1| ≤ ε
, .
- :
. 4. -
. . , . :
2. .
|
|
Program lab1;
{ }
const
lam=8.5;
hg=0.008;
Te = 953.5;
Tc = 1273;
al = 25;
en = 0.3;
c = 0.00567;
e=0.1;
var a,b,h:real;
function power(x:real;n:integer):real;
{ }
var i:integer;
step:real;
begin
step:=1;
for i:=1 to n do
step:=step*x;
power:=step;
end;
function q(T:real):real;
{ }
begin
q:=lam*(T-Te)/hg-al*(Tc-T)-en*c*(power(Tc,4)-power(T,4));
end;
function q1(T:real):real;
{ }
begin
q1:=0.006804*power(T,3)+1087.5;
end;
procedure poisk;
begin
write(' : '); readln(b);
write(' : '); readln(h);
repeat
a:=b;
b:=a+h;
until q(a)*q(b)<0;
writeln('a = ',a:0:5);
writeln('b = ',b:0:5);
end;
procedure newton(e,x1:real);
var x0,K:real;
begin
K:=q1(x1);
repeat
x0:=x1;
x1:=x0-q(x0)/K;
until abs(x0-x1)<=e;
write(' ');
writeln('T = ',x1:0:5,' q(T) = ',q(x1):0:5);
end;
begin
poisk;
newton(e,b);
readln;
end.
3. .
: . . ε .