Muhammad al-xozazmiy nomidagi toshkent axborot texnologiyalari universiteti telekommunikatsiya texnologiyalari fakulteti algoritm loyihalash

OʻZBEKISTON RESPUBLIKASI AXBOROT TEXNOLOGIYALARI VA KOMMUNIKATSIYALARINI RIVOJLANTIRISH VAZIRLIGI
MUHAMMAD AL-XOZAZMIY NOMIDAGI TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI

TELEKOMMUNIKATSIYA TEXNOLOGIYALARI FAKULTETI
ALGORITM LOYIHALASH
1-LABAROTIYA ISH

Variant: 1
Bajardi: Abdullayev Suhrobjon
Tekshirdi: Turg‘unov Abror

TOSHKENT – 2022

Aniq integralni sonli hisoblash algoritmi
№	Topshiriq
	To’g’ri to’rtburchaklar, trapetsiya va Simpson usullarida hisoblang. N bo’lish soni, E=0.001.		[0;1]	12

// 2. Aniq integralni sonli hisoblash algoritmi
//To’g’ri to’rtburchaklar, trapetsiya va Simpson usullarida hisoblang.

//Trapetsiyah

var n = 12;

function y(x) {

return Math.sin(x + 3) * Math.log(x ** 2 + 3 * x + 1)
}

function trapezoidal(a, b, n) {

let h = (b - a) / n;
let s = y(a) + y(b);
for (let i = 1; i < n; i++) s += 2 * y(a + i * h);
return (h / 2) * s;
}

let x0 = 0;

let xn = 1;

console.log( "Trapetsiya " +

Math.abs(Math.round(trapezoidal(x0, xn, n) * 10000.0) / 10000.0));

// simpson usuli

function func(x) {

return Math.sin(x + 3) * Math.log(x ** 2 + 3 * x + 1)
}

function simpsons_(ll, ul, n) {

let h = (ul - ll) / n;

let x = [];

let fx = [];

for (let i = 0; i <= n; i++) {

x[i] = ll + i * h;
fx[i] = func(x[i]);
}

let res = 0;

for (let i = 0; i <= n; i++) {
if (i == 0 || i == n) res += fx[i];
else if (i % 2 != 0) res += 4 * fx[i];
else res += 2 * fx[i];
}

res = res * (h / 3);

return res;
}

let lower_limit = 0;

let upper_limit = 1;

console.log("Simpson " + Math.abs(simpsons_(lower_limit, upper_limit, n)));

//Togri tortburchak usuli.

let n;
let a=0,b=1,h,x=0,s1=0,s0=1000000;

n=10;
while(1){
x=a;
h=(b-a)/n;
for(let i=0 ; is1+=Math.sin(x + 3) * Math.log(x ** 2 + 3 * x + 1);
x=(i+1)*h;
}
s1*=h;
if(Math.abs(s1-s0)<0.001){
console.log('Togri tortburchak:'+Math.abs(s1))

break;
}

else {
s0=s1;
s1=0;
n*=2;
}
}

1. 
   Algebraik va transtsendent tenglamalar yechimlarini
   

taqribiy usullar bilan topish.

№	Topshiriq
1.	Yechim joylashgan [a; b] oraliqni aniqlang vaoraliqni ikkiga bo’lish, vatarlar va urinmalar usuli bilan toping. E=0.001.	a) 2x­­­­­­­^3-2x-1=0 b) 3x+cosx+1=0

1. 
   Ikkiga bolish usuli
   

// 1. Yechim joylashgan [a; b] oraliqni aniqlang vaoraliqni ikkiga bo’lish, vatarlar va urinmalar usuli bilan toping. E=0.001.

// ikkiga bo'lish usuli orqali

let a=0,b=4,e=0.01;

let x,y,c;

// // 2x¬¬¬¬¬¬¬3-2x-1=0

y=2*x**3-2*x-1;

while(Math.abs(a-b)>e) {

c=(a+b)/2;

if((2*c**3-2*c-1)*(2*a**3-2*a-1)<0) {

b=c;
} else {
a=c;
}
}

console.log('ildiz '+(a+b)/2);

// urinmalar usuli

// urinmalar usuli

var a=0, b=1, e=0.01, i, x;

function f(x) {

return 2*x**3-2*x-1;
}

function f1(x) {

return 6*x*x-2;
}

function f2(x) {

return 12*x;
}

x = [];
i = 1;

if (f(a) * f2(a) > 0) {

x.push(a);
} else {
x.push(b);
}

while (true) {

x.push(x[i - 1] - f(x[i - 1]) / f1(x[i - 1]));

if (Math.abs(x[i] - x[i - 1]) < e) {

break;
}

i += 1;
}

console.log(x.length);

console.log("x=", x[i]);

//Vatarlar usuli