Ro'yxatga olish sanasi 21 Dekabr 2024
6 SotishTo‘lqin tarqalish tenglamasi uchun ayirmali sxemalar
![25# Matritsa yaratish
u := Matrix(Nx+1, Nt+1, 0):
# Boshlang‘ich shartlar
for i from 0 to Nx do
x := i*dx:
u[i+1,1] := sin(Pi*x):
u[i+1,2] := sin(Pi*x) + (dt^2/2)*c^2*(sin(Pi*(x+dx)) - 2*sin(Pi*x) +
sin(Pi*(x-dx)))/(dx^2):
end do:
# Chegaraviy shartlar
for n from 1 to Nt+1 do
u[1,n] := 0:
u[Nx+1,n] := 0:
end do:
# Ayirmali sxema orqali hisoblash
for n from 2 to Nt do
for i from 2 to Nx do
u[i,n+1] := 2*u[i,n] - u[i,n-1] + r*(u[i+1,n] - 2*u[i,n] + u[i-1,n]):
end do:
end do:
# sonli yechim
printf(" t = 0.05 uchun sonli yechim:\n"):
nval := trunc(0.05/dt):
for i from 0 to Nx do
printf("x = %.1f, u(x,t=0.05) = %.5f\n", i*dx, u[i+1,nval]):
end do:](https://docx.uz/documents/35ff5b83-94e6-4fcf-b456-1870f00fe4bf/page_25.png?v=1)
![26# grafigi
frame := []:
for n from 1 to Nt by 10 do
data := [seq([i*dx, u[i+1,n]], i=0..Nx)]:
frame := [op(frame), plot(data, style=line, color=red, thickness=2)]:
end do:
display(frame, insequence=true, title="To‘lqin tenglamasi yechimi (1-
masala)")
Dastur natijasi:](https://docx.uz/documents/35ff5b83-94e6-4fcf-b456-1870f00fe4bf/page_26.png?v=1)
![28Dastur kodi:
restart;
with(plots);
L := 2;
c := 2;
dx := 0.2;
dt := 0.01;
Nx := trunc(L/dx);
Nt := 100;
r := (c*dt/dx)^2;
u := Matrix(Nx + 1, Nt + 1, 0);
for i from 0 to Nx do
x := i*dx;
u[i + 1, 1] := x*(2 - x);
u[i + 1, 2] := u[i + 1, 1] + dt^2/2*c^2*((x + dx)*(2 + (-x - dx)) -
2*x*(2
- x) + (x - dx)*(2 + (-x + dx)))/dx^2;
end do;
for n to Nt + 1 do
u[1, n] := 0;
u[Nx + 1, n] := 0;
end do;
for n from 2 to Nt do
for i from 2 to Nx do u[i, n + 1] := 2*u[i, n] - u[i, n - 1] + r*(u[i + 1,
n] - 2*u[i, n] + u[i - 1, n]); end do;
end do;
printf("t = 0.1 uchun sonli natijalar:\n");](https://docx.uz/documents/35ff5b83-94e6-4fcf-b456-1870f00fe4bf/page_28.png?v=1)
![29nval := trunc(0.1/dt);
for i from 0 to Nx do
printf("x = %.1f, u(x,t=0.1) = %.5f\n", i*dx, u[i + 1, nval]);
end do;
frame := [];
for n by 10 to Nt do
data := [seq([i*dx, u[i + 1, n]], i = 0 .. Nx)];
frame := [op(frame), plot(data, style = line, color = blue, thickness =
2)];
end do;
display(frame, insequence = true, title = "To‘lqin tenglamasi
yechimi (2-masala)");
Dastur natijasi:](https://docx.uz/documents/35ff5b83-94e6-4fcf-b456-1870f00fe4bf/page_29.png?v=1)
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