Oʻzbekiston respublikasi axborot texnologiyalari va kommunikatsiyalarini rivojlantirish vazirligi muhammad al-xozazmiy nomidagi toshkent axborot texnologiyalari universiteti kif 211-20-guruh talabasi O’rinxo’jayev Azizxonning

Algebraik va transtsendent tenglamalar yechimlarini taqribiy usullar bilan topish.

1.15.

Yechim joylashgan [a; b] oraliqni aniqlang vaoraliqni ikkiga bo’lish, vatarlar va urinmalar usuli bilan toping. E=0.001.

a) x­­­­­­­^3-x+2=0 b) sin(x/2)+1=x^2

Dastur kodi:

// my function f(x)= x­­­­­­­³-x+2; f1(x) = (x­­­­­­­³-x+2)`
const f = x => x**3-x+2;
const f1 = x => 3*x**2-1;
const f2 = x => 6*x;

// Oraliqni teng ikkiga bo’lish usuli:

const func1 = (a,b,e) => {
do{
let c = (a+b)/2;
f(a)*f(c)<0 ? b=c : a=c;
}while(b-a>e)
return (a+b)/2
}
console.log(func1(-2,0,0.001));
result: -1.6363636363636362

// Urunmalar usuli:

const func2 = (a,b,e) => {
let x0=0,x=0;
let c = a-f(a)*((b-a)/(f(b)-f(a)));

f(a)*f(c)<0 ? x0=a : x0=b;

do{
x=x0-(f(x0)/f1(x0))

x0=x;
}while(-(f(x0)/f1(x0))

return x;

}
console.log(func2(-2,0,0.001));
result: -1.62099609375

// Vatarlar usuli:

#include
#include
using namespace std;
float F (float x){return pow(x,3)-x+2;}
float F1 (float x){return 3*pow(x,2)-1;}
float F2(float x){return 6*x;}
int main(){
float a=-1, b=0, S = 0, x1, x2, eps=0.001;
if(F1(a) * F2(a) > 0) x1 = a;
else goto _2;
_1: x2 = x1 - F(x1) * (b - x1) / (F(b) - F(x1));
if(F1(a) * F2(a) < 0) x1 = b;
if(abs(x2 - x1) > eps){
x1 = x2;
goto _1;
}
else goto _3;
_2: if(F1(a) * F2(a) < 0) x1 = b;
_4: x2 = x1 - F(x1) * (x1 - a) / (F(x1) - F(a));
if(abs(x1 - x2) > eps){
x1 = x2;
goto _4;
}
_3: cout << x1;
return 0;
}
Result: -1.6102345445

2. Aniq integralni sonli hisoblash algoritmi

To’g’ri to’rtburchaklar, trapetsiya va Simpson usullarida hisoblang. N bo’lish soni, E=0.001.

[1;2]

12

Dastur kodi:

// my function f(x) = ∛(x^2+3x+1)∙e^(〖-x〗^2 )

const f = (x) => Math.pow((x**2+3*x+1),1/3)*Math.E**(-(x**2));

// to'rtburchaklar usuli
const func = (a,b,n) => {
let x=0, h = (b-a)/n;

for(let i=1; i<=n; i++){

x += f(a+i*h)*h;
}
return x;
}
console.log(func(1,2,1000));
result: 0.2523365234751908

// trapetsiya usuli

const func1 = (a,b,n) => {
let x=0, sum=0, h = (b-a)/n;

for(let i=1; i
x=a+i*h
sum += 2*f(x);
}
return (h/2)*(sum + f(a) + f(b));
}
console.log(func1(1,2,1000));
result: 0.25263068916491344

// simson usuli

const integral2 = (a,b,n) => {
let sum = 0;
let m =n/2;
let h = (b-a)/n;
for(let i=1; i<=m; i++){
sum += 4*f(a+(2*i-1)*h) + (i!==n/2 && 2*f(a+(2*i)*h));
}
return (sum + f(a) + f(b))*h/3;
}

console.log(integral2(1,2,10));

result: 0.25263061465257103