Issiqlik o‘tkazuvchanlik masalalarini chekli ayirmali sxemalar
![Chegaraviy masalalarni yechishning sonli usullarini qaraymiz. Ularni ikkita
guruhga ajratish mumkin:
1) Chegaraviy masala echimini ketma-ket Koshi masalalarini echishga
keltirish;
2) Chekli ayirmalar usullarini qo`llash.
Birinchi guruh usullariga, xususan, o`q otish usuli kiradi.
O`q otish usuli
[0,1] kesmada ikkinchi hosilaga nisbatan echilgan ikkinchi tartibli tenglama
uchun chegaraviy masalani qaraymiz:
(1 6) H ar qanday kesmani
almashtirish yordamida [0,1] kesmaga keltirish mumkin .
CHegaraviy shartni quyidagi oddiy ko ` rinishda olamiz
. (17)
O ` q otish usulining mo і iyati (1), (2) chegaraviy masalani echishni (1)
tenglama uchun
(18)
boshlang ` ich shartli masala echimiga
keltirishdan iborat , bunda - parametr
nuqtada integral chiziqga
o`tkazilgan urinmaning o`qi bilan
hosil qilgan burchagidir .
130 11 y(x,
)y(x,
1 )
xy
0y
y
1](https://docx.uz/documents/52711c27-f37a-41b2-99a9-e03ecbcb60dc/page_13.png?v=1)
![{
float fnf;
fnf=sin(3.14159*x);
return fnf;
}
float fnf1 (float t)
{
float fnf1;
fnf1=0;
return fnf1;
}
float fnf2(float t);
{
float fnf2;
fnf2=0;
return fnf2;
}
int main(int argc, char *argv[])
{
float y,h,a,b,t1,c,d,g,w,e,s,k;
int n,m,i,j;
"float x[60],t[60],u[60][60];
cin>>a>>b;
cin>>h;
23](https://docx.uz/documents/52711c27-f37a-41b2-99a9-e03ecbcb60dc/page_23.png?v=1)
![cin>>t1;
k=h*h/2;"
for(i=0;i<=n;i++)
{
x[i]=i*h;
cout<<" "<<x[i];
}
for(j=0;i<=2*m;j++)
for(i=0;i<=2*n;i++)
{
t[j]=j*k;
u[0,j]=fnf1(t[j]);
u[n,j]=fnf2(t[j])
x[i]=i*n;
u[i,0]=fnf(x[i]);
for(j=0;j<=2*m;j++)
for(i=1;i<=2*n;i++)
u[i,j+1]=(u[i-1,j]+u[i+1,j])/2;
for(j=0;j<=m;j++)
{
t[j]=j*k;
"cout<<t[j];"
for(i=0;i<=n;i++)
"cout<<u[i,j];"
24](https://docx.uz/documents/52711c27-f37a-41b2-99a9-e03ecbcb60dc/page_24.png?v=1)
Issiqlik o‘tkazuvchanlik masalalarini chekli ayirmali sxemalar