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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 .



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