Mavzu: Tenglamalar sestemasini yechishning Zeydel va Nyuton usuli

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Mavzu Tenglamalar sestemasini yechishning Zeydel va Nyuton usul

CHIZIQSIZ TENGLAMALAR SISTEMASINI TAQRIBIY YECHISHDA NYUTON USULI

Muhammad al-Xorazmiy nomidagi Toshkint axborot texnalogiyalari universituti.

3-Labaratoriya ishi
Mavzu:Tenglamalar sestemasini yechishning Zeydel va Nyuton usuli

Bajardi:Abdullayeva.N

Tekshirdi:Akbaraliyev.B

CHIZIQSIZ TENGLAMALAR SISTEMASINI TAQRIBIY YECHISHNI ANIQLIKDA ZEYDEL USULI BILAN TOPISH

#include
#include
using namespace std;
int main ()
{
float a[100], b[100], c[100];
int i=0;
a[0]=65*1./12;
b[0]=78*1./10;
c[0]=41*1./9;
a[i+1]=65*1./12-3*1./12*b[i]-4*1./12*c[i];
b[i+1]=78*1./10-2*1./10*a[i+1]-1*1./10*c[i];
c[i+1]=41*1./9-3*1./9*a[i+1]-2*1./9*b[i+1];
cout<<"\n\t"<while(sqrt(pow((a[i+1]-a[i]),2)+pow((b[i+1]-b[i]),2)+pow((c[i+1]-c[i]),2))>=0.001)
{
i=i+1;
a[i+1]=65*1./12-3*1./12*b[i]-4*1./12*c[i];
b[i+1]=78*1./10-2*1./10*a[i+1]-1*1./10*c[i];
c[i+1]=41*1./9-3*1./9*a[i+1]-2*1./9*b[i+1];
cout<}
cout<<"ANIQLIK: "<cout<<" Yechim: "<<12*a[i+1]+3*b[i+1]+4*c[i+1]<<"\n\t";
return 0;
}

A B C D E F G

0	5,416667	7,8	4,555556
1	1,948148	6,954815	2,360658	3,468519	0,845185	2,194897
2	2,891077	6,985719	2,039481	0,942929	0,030904	0,321177
3	2,99041	6,99797	2,003648	0,099333	0,012251	0,035833
4	2,999292	6,999777	2,000286	0,008882	0,001807	0,003362
5	2,999961	6,999979	2,000018	0,000669	0,000202	0,000268

CHIZIQSIZ TENGLAMALAR SISTEMASINI TAQRIBIY YECHISHDA NYUTON USULI

Quyidagi ko‘rinishdagi sistema berilgan bo‘lsin.

(1)

Biz buyerda sistemaning yagona yechimi mavjud bo‘lgan soha D ma’lum deb hisoblaymiz. Shu sohadagi taqribiy yechimni berilgan >0 aniqlikda topish uchun quyidagi iteratsion jarayon tatbiq qilinadi. Avvalo boshlang‘ich yaqinlashish tanlanadi. Keyingi qadamlar esa quyidagi formulalar bilanhisoblanadi.

(2)

Bu yerda

(3)

(8) formulalarda funksiyalar va ularning hosilalarining qiymatlari nuqtada hisoblanadi. (7) formulalar bo‘yicha hisoblashlar esa talab qilingan aniqlik bajarilguncha, ya’ni

(4)

Shart bajarilguncha davom ettiriladi.

	2-topshiriq
Variant raqami	Chiziqsiz tenglamalar sistemasi yechimini Nyuton usuli bilan toping
1	D={x>0; y>0} E=0.004

Misol

Yechilishi
bu yerda f1(x,y)= f2(x,y)=

x	y	d	d1	d2	E
1	0,5	2	-8,25	1
5,125	0	10,25	17,26563	-31,9688	4,155192535
3,4405488	3,118902	37,32843	30,26393	41,80638	3,544704266
2,6298015	1,998942	18,29111	4,539477	2,773937	1,382614702
2,3816221	1,847287	14,97225	0,312152	-0,05963	0,290847377
2,3607734	1,85127	14,79818	0,00206	-0,00083	0,02122574
2,3606342	1,851325	14,79718	9,42E-08	-3E-08	0,000149978

#include

using namespace std;
int main()
{
float f1,f2,f1xhosila,f2xhosila,f1yhosila,f2yhosila,D, D1, D2,x[10],y[10];
int n;
cout<cout<<"Ikkita chiziqsiz tenglamalar sistemasini taqribiy yechishda NYUTON usuli"<cout<x[0]=1; y[0]=0.5;
for(n=0; ;n++)
{
f1=pow(x[n],2)-2*x[n]-y[n]+1;
f2=pow(x[n],2)+pow(y[n],2)-9;
f1xhosila=2*x[n]-2;
f1yhosila=-1;
f2xhosila=2*x[n];
f2yhosila=2*y[n];
D=f1xhosila*f2yhosila-f1yhosila*f2xhosila;
D1=f1*f2yhosila-f2*f1yhosila;
D2=f2*f1xhosila-f1*f2xhosila;
x[n+1]=x[n]-D1/D;
y[n+1]=y[n]-D2/D;
cout<<"x["<Download 104,31 Kb.
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