Guruh Abdurashidov Bexruz

2-amaliy ishi.
Mavzu: Algebraik va transtendent tenglamalarni yechishda oraliqni teng ikkiga bo’lish, iterasiya usullari. Tenglamalarni yechishda vatarlar va Nyuton usullari. Yaqinlashish tezligi

Berilgan topshiriq:

1. Aniqlangan oraliqda ildizning taqribiy qiymatini 0.001 aniqlikda hisoblang.
2. Kesmani teng ikkiga bo‘lish usuli bilan taqribiy hisoblang.


1. Dastur kodi:

let kesmaniTengIkkigaBoLish = (a, b, epsilon) => {

let x1, x2, y1, y2;
x1 = a;
y1 = tan(0.58x+0.1) – Math.pow(x,2);

let k = 0;

while (true) {
k++;
x2 = a + (b - a) / Math.pow(2, k);
y2 = tan(0.58x+0.1) – Math.pow(x,2);
if (Math.abs(y2 - y1) < epsilon) {
break;
}
x1 = x2;
y1 = y2;
}
return (x1 + x2) / 2;
}

let a = 0.5;

let b = 1.0;
let epsilon = 0.001;

let x = kesmaniTengIkkigaBoLish(a, b, epsilon);

console.log("Tenglama yechimi: x =", x);
Algoritmi:
1.1. x1, y1 o'zgaruvchilarni a qiymati bilan aniqlang va x1 qiymatini x1, y1 blokida saqlang.
1.2. k=0 deb olamiz.
1.3. "while" tsiklida toki x2 = a + (b - a) / 2^k ni hisoblash.
1.4. y2 qiymatini tan(0.58 * x2 + 0.1) - x2^2 hisobidan toping.
1.5. y2-y1 ni epsilon dan kichikligini tekshiring.
1.6. Agar epsilon dan kichik bo'lsa tsiklni to'xtating.
1.7. x1 = x2, y1 = y2.
1.8. x1 va x2 o'zgaruvchilar yordamida tenglamani yeching.
1.9. Yakunida x qiymatini qaytarish.
Tenglama yechimi: 0.500183

x3 -0.2x2+0.5x-1.4=0

Bajaralishi tartibi:

1.Dastur kodi:
function f(x) {
return Math.pow(x, 3) - 0.2 * Math.pow(x, 2) + 0.5 * x - 1.4;
}

let a = 0, b = 1.5, eps = 0.001;

let c, fc;

while (b - a > eps) {

c = (a + b) / 2;
fc = f(c);

if (fc == 0) {

break;
} else if (f(a) * fc < 0) {
b = c;
} else {
a = c;
}
}
cout << "Tenglamaning yechimi: " << c << endl;
return 0;
}
Natija:
Start
|
v
Define f(x)
|
v
Initialize a, b, eps
|
v
While (b - a > eps)
|
|----- Calculate c = (a + b) / 2
|
|----- Calculate fc = f(c)
|
|----- If (fc == 0)
| |
| v
|----- break
|
|----- Else if (f(a) * fc < 0)
| |
| v
|----- b = c
|
|----- Else
|
v
----- a = c
|
v
Output c as the root of f(x)
|
v
End